ALBERT

Description:    We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems. Content Type Journal Article Pages 547-566 DOI 10.1007/s11232-011-0041-y Authors J. Brüning, Humboldt University, Berlin, Germany V. V. Grushin, Moscow State Institute for Electronics and Mathematics, Moscow, Russia S. Yu. Dobrokhotov, Moscow Institute for Physics and Technology, Moscow, Russia T. Ya. Tudorovskii, Institute for Molecules and Materials Radboud, University of Nijmegen, Nijmegen, The Netherlands Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We present the bi-Hamiltonian structure and Lax pair of the equation ρ t = bu x +( 1/2 )[(u 2 −u x 2 )ρ] x , where ρ = u − u xx and b = const , which guarantees its integrability in the Lax pair sense. We study nonsmooth soliton solutions of this equation and show that under the vanishing boundary condition u → 0 at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions. Content Type Journal Article Pages 584-589 DOI 10.1007/s11232-011-0044-8 Authors Zhijun Qiao, Department of Mathematics, The University of Texas-Pan American, Edinburg, Texas, USA Xianqi Li, Department of Mathematics, The University of Texas-Pan American, Edinburg, Texas, USA Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We study the Wigner function in noncommutative quantum mechanics. By solving the time-independent Schrödinger equation on both a noncommutative space and a noncommutative phase space, we obtain the Wigner function for the Landau problem on those spaces. Content Type Journal Article Pages 628-635 DOI 10.1007/s11232-011-0047-5 Authors S. Dulat, School of Physics Science and Technology, Xinjiang University, Urumqi, China Kang Li, Department of Physics, Hangzhou Normal University, Hangzhou, China Jianhua Wang, Department of Physics, Shaanxi University of Technology, Hanzhong, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for p-adic closed and open strings in the tree approximation in the case d = 1 . For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign. Content Type Journal Article Pages 539-546 DOI 10.1007/s11232-011-0040-z Authors V. S. Vladimirov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    Based on number theory, we present a new concept of gas without the particle interaction taken into account in which there are first-order phase transitions for T 〈 T cr on isotherms. We present formulas for new ideal gases, solving the Gibbs paradox, and also formulas for the transition to real gases based on the concept of the Zeno line. Content Type Journal Article Pages 654-667 DOI 10.1007/s11232-011-0050-x Authors V. P. Maslov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We establish that by choosing a smooth local perturbation of the boundary of a planar quantum waveguide, we can create an eigenvalue near any given threshold of the continuous spectrum and the corresponding trapped wave exponentially decaying at infinity. Based on an analysis of an auxiliary object, a unitary augmented scattering matrix, we asymptotically interpret Wood’s anomalies, the phenomenon of fast variations in the diffraction pattern due to variations in the near-threshold wave frequency. Content Type Journal Article Pages 606-627 DOI 10.1007/s11232-011-0046-6 Authors S. A. Nazarov, Institute of Mechanical Engineering Problems, RAS, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    Starting from the matrix KP hierarchy and adding a new τ B flow, we obtain a new extended matrix KP hierarchy and its Lax representation with the symmetry constraint on squared eigenfunctions taken into account. The new hierarchy contains two sets of times t A and τ B and also eigenfunctions and adjoint eigenfunctions as components. We propose a generalized dressing method for solving the extended matrix KP hierarchy and present some solutions. We study the soliton solutions of two types of ( 2+1 )-dimensional AKNS equations with self-consistent sources and two types of Davey-Stewartson equations with selfconsistent sources. Content Type Journal Article Pages 590-605 DOI 10.1007/s11232-011-0045-7 Authors Yehui Huang, Department of Mathematical Science, Tsinghua University, Beijing, China Xiaojun Liu, Department of Applied Mathematics, China Agricultural University, Beijing, China Yuqin Yao, Department of Applied Mathematics, China Agricultural University, Beijing, China Yunbo Zeng, Department of Mathematical Science, Tsinghua University, Beijing, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We propose a model on the Cayley tree and prove that a uncountable set of Ĝ-periodic Gibbs measures exists for this model, in contrast to models studied previously. Content Type Journal Article Pages 668-679 DOI 10.1007/s11232-011-0051-9 Authors U. A. Rozikov, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan G. T. Madgoziev, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We propose a construction of a Lagrangian torus fibration of the full flag variety in ℂ 3 . In contrast to the classical fibration obtained from the Gelfand-Zeitlin system, the proposed fibration is special Lagrangian. Content Type Journal Article Pages 567-576 DOI 10.1007/s11232-011-0042-x Authors N. A. Tyurin, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We propose a method for describing quasiequilibrium processes in a quasistable anharmonic oscillator affected by heat noise. We introduce effective thermodynamic parameters analogous to those of an equilibrium system but differing from them in numerical value. We define the parameter characterizing the nonequilibrium of the system, prove the mathematical consistency of the proposed method, and obtain the quasiequilibrium analogue of the theorem on energy distribution over degrees of freedom. Content Type Journal Article Pages 636-644 DOI 10.1007/s11232-011-0048-4 Authors A. V. Kargovsky, Lomonosov Moscow State University, Moscow, Russia L. S. Bulushova, Lomonosov Moscow State University, Moscow, Russia O. A. Chichigina, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We develop the recent proposal to use dimensional reduction from the four-dimensional space-time (D = 1 + 3 ) to the variant with a smaller number of space dimensions D = 1 + d, d 〈 3, at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation with a few toy examples (“educational toys”) of a space-time with a variable spatial geometry including a transition to a dimensional reduction. The examples considered contain a combination of two regions with a simple geometry (two-dimensional cylindrical surfaces with different radii) connected by a transition region. The new technique for transforming the study of solutions of the Klein-Gordon problem on a space with variable geometry into solution of a one-dimensional stationary Schrödinger-type equation with potential generated by this variation is useful. We draw the following conclusions: ( 1 ) The signal related to the degree of freedom specific to the higher-dimensional part does not penetrate into the smaller-dimensional part because of an inertial force inevitably arising in the transition region (this is the centrifugal force in our models). ( 2 ) The specific spectrum of scalar excitations resembles the spectrum of real particles; it reflects the geometry of the transition region and represents its “fingerprints.” ( 3 ) The parity violation due to the asymmetric character of the construction of our models could be related to the CP symmetry violation. Content Type Journal Article Pages 680-691 DOI 10.1007/s11232-011-0052-8 Authors P. P. Fiziev, Sofia University St. Kliment Ohridski, Sofia, Bulgaria D. V. Shirkov, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass-glass transition. Content Type Journal Article Pages 645-653 DOI 10.1007/s11232-011-0049-3 Authors V. N. Ryzhov, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia E. E. Tareyeva, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia Yu. D. Fomin, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We consider two initial boundary value problems on an interval with homogeneous Dirichlet conditions. These problems were proposed by M. I. Rabinovich and D. I. Trubetskov and are given by nonlinear fourth-order Sobolev-type equations. We prove the local-in-time existence of a strong generalized solution of one problem, and for both problems, we obtain sufficient conditions for the destruction of their strong generalized solutions in a finite time. Content Type Journal Article Pages 577-583 DOI 10.1007/s11232-011-0043-9 Authors M. O. Korpusov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Description:    We consider the evolution of the spatial distribution of fast atomic particles as they pass through a crystal. At small penetration depths where the particles move without significant loss of coherence, the joint probability density function becomes smoother at the expense of the gradient of the anharmonic potential of the planar channel. We show that as a result of this smoothing, there arises a quasiequilibrium (quasistationary) state of the subsystem of fast particles. The further evolution of the particle distribution is caused by nonelastic scattering and is described by the kinetic equation. At this stage, the anharmonic character of particle oscillations between the channel walls results in a renormalization of the total phonon scattering cross section of particles, and the renormalization is determined by the fourth-order anharmonic interaction. Content Type Journal Article Pages 506-516 DOI 10.1007/s11232-011-0038-6 Authors Yu. A. Kashlev, Baikov Institute for Metallurgy and Material Science, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Description:    We propose a method for calculating vacuum means of the scalar field energy-momentum tensor on Lie groups and homogeneous spaces. We use the generalized harmonic analysis based on the method of coadjoint representation orbits. Content Type Journal Article Pages 468-483 DOI 10.1007/s11232-011-0035-9 Authors A. I. Breev, Tomsk State University, Tomsk, Russia I. V. Shirokov, Omsk State Technical University, Omsk, Russia A. A. Magazev, Irtysh Branch of Novosibirsk State Academy of Water Transport, Novosibirsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Description:    We construct the group bundle for the inverse Fibonacci semigroups in the axiomatic approach framework. The proper Fibonacci semigroup is the corresponding group bundle for the Penrose semigroups, which can be interpreted as the generating grammar of the morphogenetic synthesis of the pentasymmetric Penrose parquet in the numbers of tiling by golden rhombuses. This morphogenetic synthesis of the Penrose parquet satisfies the scaling principle. Parquet plates are not absolutely rigid, and the relations between their metric characteristics are governed by the golden section and other magic numbers. The characteristic form factors of three-level dual alphabets are the corresponding invariants. We realize the morphogenetic synthesis in the examples of square-octagonal and bihexagonal lattices. We consider cumulative properties of magic series and the evolutionary aspects of semigroup orbits in the entropy representation. Content Type Journal Article Pages 517-537 DOI 10.1007/s11232-011-0039-5 Authors V. V. Yudin, Far-East State University, Vladivostok, Russia E. S. Startzev, Far-East State University, Vladivostok, Russia I. G. Permyakova, Far-East State University, Vladivostok, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Description:    We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system. Content Type Journal Article Pages 496-505 DOI 10.1007/s11232-011-0037-7 Authors A. A. Khamzin, Kazan State Energy University, Kazan, Russia R. R. Nigmatullin, Kazan (Volga Region) Federal University, Kazan, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Description:    We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler-Bobenko-Suris equations. Content Type Journal Article Pages 421-443 DOI 10.1007/s11232-011-0033-y Authors A. V. Mikhailov, Applied Mathematics Department, University of Leeds, Leeds, UK Jing Ping Wang, School of Mathematics and Statistics, University of Kent, Kent, UK P. Xenitidis, Applied Mathematics Department, University of Leeds, Leeds, UK Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Description:    We propose a Lie-Noether-symmetry solution of two problems that arise with classical quantization: the quantization of higher-order (more than second) Euler-Lagrange ordinary differential equations of classical mechanics and the quantization of any second-order Euler-Lagrange ordinary differential equation that classically comes from a simple linear equation via nonlinear canonical transformations. Content Type Journal Article Pages 994-1001 DOI 10.1007/s11232-011-0081-3 Authors M. C. Nucci, Dipartimento di Matematica e Informatica, Università di Perugia and INFN, Sezione di Perugia, Perugia, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Description: Nonlinear physics: Theory and experiment VI Content Type Journal Article Pages 857-857 DOI 10.1007/s11232-011-0068-0 Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Description:    We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearity into account. We develop a method for transforming Maxwell’s equations based on a complete set of projection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with the propagation direction taken into account. The most important result of applying the method is a system of equations describing the one-dimensional dynamics of pulses propagating in opposite directions without accounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersion in the media and show how the operators change. We obtain generalized Schäfer-Wayne short-pulse equations accounting for both propagation directions. In the three-dimensional problem, we focus on optic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-mode interaction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinear Schrödinger equations, we discuss a concept of numerical integrability and apply the developed calculation schemes. Content Type Journal Article Pages 974-984 DOI 10.1007/s11232-011-0079-x Authors M. Kuszner, Gdansk University of Technology, Gdansk, Poland S. Leble, Gdansk University of Technology, Gdansk, Poland B. Reichel, Gdansk University of Technology, Gdansk, Poland Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Description:    We study properties of the purely solitonic τ-function and potential of the heat equation in detail. We describe the asymptotic behavior of the potential and establish the ray structure of this asymptotic behavior on the plane (x 1 , x 2 ) in dependence on the parameters of the potential. Content Type Journal Article Pages 865-874 DOI 10.1007/s11232-011-0070-6 Authors M. Boiti, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy F. Pempinelli, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy A. K. Pogrebkov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Description:    We briefly review the half-a-century period (1959–2009) of the creation, development, and application of the method of two-time temperature retarded and advanced Green’s functions, introduced by Bogoliubov and Tyablikov in 1959. This method has not exhausted its resources by far, as is evidenced by its effective modification proposed by Plakida in 1970 and Tserkovnikov in 1971 and then, in a much more advanced form, by Tserkovnikov in 1981. Currently, a self-consistent description of both one-particle (transverse) and collective (longitudinal) Green’s functions and correlation functions is achieved based on the Green’s function method in the Bogoliubov-Tyablikov-Plakida-Tserkovnikov formulation. Content Type Journal Article Pages 1318-1329 DOI 10.1007/s11232-011-0108-9 Authors Yu. G. Rudoy, Peoples’ Friendship University of Russia, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 3

Description:    We apply the Bogoliubov-Tyablikov method of two-time Green’s functions to a multielectron theory of metals in the framework of the models with strong correlations, which are the Hubbard model and the Vonsovskii s-d(f) exchange model. We discuss the atomic representation in the problem of describing electron states, the metal-insulator transition, the problem of noncoherent states, and the Kondo effect. We analyze the ferromagnetism criterion in systems of strongly correlated electrons, which differs drastically from the Stoner condition. Content Type Journal Article Pages 1246-1257 DOI 10.1007/s11232-011-0102-2 Authors V. Yu. Irkhin, Institute of Metal Physics, Ural Branch, RAS, Ekaterinburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 3

Description:    We review the problem of ambiguity in quantizing non-Abelian gauge theories and propose a method for quantizing them unambiguously. Content Type Journal Article Pages 198-202 DOI 10.1007/s11232-012-0021-x Authors A. A. Slavnov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 2

Description:    Motivated by claims of broken rotational invariance in the WMAP data, a number of models have appeared in the literature realizing this effect through vector field(s) with a nonvanishing spatial vacuum expectation value. We discuss why many such models have ghost instabilities. Content Type Journal Article Pages 181-186 DOI 10.1007/s11232-012-0019-4 Authors M. Peloso, School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota, USA Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 2

Description: In memory of A. N. Tavkhelidze Content Type Journal Article Pages 131-131 DOI 10.1007/s11232-012-0014-9 Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 2

Description:    We discuss a two-component liquid model for the quark-gluon plasma. We show that the model explains the basic experimental observations of the plasma properties naturally on the qualitative level. From the standpoint of the dynamics, the model assumes the existence of an effective scalar field with a nonzero vacuum expectation value. The hypothesis that such a condensate exists is supported by lattice data. We formulate the kind of lattice data that would yield a possible verification of the model. Content Type Journal Article Pages 211-216 DOI 10.1007/s11232-012-0023-8 Authors M. N. Chernodub, Laboratoire de Mathématiques et Physique Théorique, Université Francois-Rabelais de Tours, Tours, France H. Verschelde, Department of Physics and Astronomy, Ghent University, Ghent, Belgium V. I. Zakharov, Institute of Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 2

Description:    We consider two versions of the scenario for generating scalar cosmological perturbations based on the conformal symmetry: a spectator version with a scalar field conformally coupled to gravity and with a negligible energy density; a dynamical version with a scalar field minimally coupled to gravity and dominating the cosmological evolution. Using the Newtonian gauge, we show, first, that no UV strong-coupling scale is generated below M Pl , because of mixing with metric perturbations in the dynamical scenario, and, second, that both the dynamical and the spectator models yield identical results in the leading nonlinear order. These results, which include potentially observable effects like statistical anisotropy and non-Gaussianity, hold for the entire class of conformal models. As an example, in the dynamical scenario with the comoving gauge, we reproduce our result on the statistical anisotropy, previously obtained in the framework of the spectator approach. Content Type Journal Article Pages 1457-1465 DOI 10.1007/s11232-012-0126-2 Authors M. V. Libanov, Institute for Nuclear Research, RAS, Moscow, Russia V. A. Rubakov, Institute for Nuclear Research, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant. Content Type Journal Article Pages 1377-1386 DOI 10.1007/s11232-012-0120-8 Authors U. A. Rozikov, Institute of Mathematics at National University of Uzbekistan, Tashkent, Uzbekistan R. M. Khakimov, Institute of Mathematics at National University of Uzbekistan, Tashkent, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We consider the problem of the effective interaction potential in a quantum many-particle system leading to the fractional-power dispersion law. We show that passing to fractional-order derivatives is equivalent to introducing a pair interparticle potential. We consider the case of a degenerate electron gas. Using the van der Waals equation, we study the equation of state for systems with a fractional-power spectrum. We obtain a relation between the van der Waals constant and the phenomenological parameter α, the fractional-derivative order. We obtain a relation between energy, pressure, and volume for such systems: the coefficient of the thermal energy is a simple function of α. We consider Bose—Einstein condensation in a system with a fractional-power spectrum. The critical condensation temperature for 1 〈 α 〈 2 is greater in the case under consideration than in the case of an ideal system, where α = 2. Content Type Journal Article Pages 1445-1456 DOI 10.1007/s11232-012-0125-3 Authors Z. Z. Alisultanov, Prokhorov General Physics Institute, RAS, Moscow, Russia R. P. Meilanov, Institute of Geothermal Problems, Dagestan Scientific Center, RAS, Makhachkala, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We show that the Weyl correspondence and the concept of a Moyal multiplier can be naturally extended to generalized function classes that are larger than the class of tempered distributions. This generalization is motivated by possible applications to noncommutative quantum field theory. We prove that under reasonable restrictions on the test function space E ⊂ L 2 , any operator in L 2 with a domain E and continuous in the topologies of E and L 2 has a Weyl symbol, which is defined as a generalized function on the Wigner-Moyal transform of the projective tensor square of E. We also give an exact characterization of the Weyl transforms of the Moyal multipliers for the Gel’fand-Shilov spaces S β β . Content Type Journal Article Pages 1359-1376 DOI 10.1007/s11232-012-0119-1 Authors M. A. Soloviev, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We propose a uniform method for estimating fractal characteristics of systems satisfying some type of scaling principle. This method is based on representing such systems as generating Bethe-Cayley tree graphs. These graphs appear from the formalism of the group bundle of Fibonacci-Penrose inverse semigroups. We consistently consider the standard schemes of Cantor and Koch in the new method. We prove the fractal property of the proper Fibonacci system, which has neither a negative nor a positive redundancy type. We illustrate the Fibonacci fractal by an original procedure and in the coordinate representation. The golden ratio and specific inversion property intrinsic to the Fibonacci system underlie the Fibonacci fractal. This property is reflected in the structure of the Fibonacci generator. Content Type Journal Article Pages 1387-1402 DOI 10.1007/s11232-012-0121-7 Authors V. V. Yudin E. S. Startzev, Institute for Physics and Information Technologies, Far-East Federal University, Vladivostok, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We consider classical aspects of the dynamics of scalar fields with nonpositive-definite potentials in the Friedmann cosmology. Such models appear as effective local models in the framework of nonlocal models related to string field theory. In an effective local approximation after a suitable field redefinition, the Higgs potential with a negative effective cosmological constant appears in these models. A special feature of considered models is an absence of the reheating phase, instead of which phase of regime change from expansion to contraction appears. We study the behavior of the model near the point of regime change. Content Type Journal Article Pages 1466-1480 DOI 10.1007/s11232-012-0127-1 Authors I. Ya. Arefeva, Steklov Mathematical Institute, RAS, Moscow, Russia N. V. Bulatov, Lomonosov Moscow State University, Moscow, Russia R. V. Gorbachev, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We construct a family of two-gap solutions of the focusing nonlinear Schrödinger equation and derive a condition under which the solutions behave as the so-called freak waves located at the nodes of a two-dimensional lattice. We also study how the lattice parameters depend on the parameters of the spectral curve. Content Type Journal Article Pages 1403-1416 DOI 10.1007/s11232-012-0122-6 Authors A. O. Smirnov, St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We consider perturbations of a second-order periodic operator on the line; the Schrödinger operator with a periodic potential is a specific case of such an operator. The perturbation is realized by a potential depending on two small parameters, one of which describes the length of the potential support, and the inverse value of other corresponds to the value of the potential. We obtain sufficient conditions for the perturbing potential to have eigenvalues in the gaps of the continuous spectrum. We also construct their asymptotic expansions and present sufficient conditions for the eigenvalues of the perturbing potential to be absent. Content Type Journal Article Pages 1438-1444 DOI 10.1007/s11232-012-0124-4 Authors R. R. Gadylshin, Akmulla Bashkir State Pedagogical University, Ufa, Russia I. Kh. Khusnullin, Akmulla Bashkir State Pedagogical University, Ufa, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We briefly review problems arising in the study of the beta deformation, which turns out to be the most difficult element in a number of modern problems: the deviation of β from unity is connected with the “exit from the free-fermion point” in two-dimensional conformal theories, from the symmetric graviphoton field with ∈ 2 = −∈ 1 in instanton sums in four-dimensional supersymmetric Yang-Mills theories, with the transition from matrix models to beta ensembles, from HOMFLY polynomials to superpolynomials in the Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras, and so on. We mainly attend to issues related to the Alday-Gaiotto-Tachikawa correspondence and its possible generalizations. Content Type Journal Article Pages 1417-1437 DOI 10.1007/s11232-012-0123-5 Authors A. Yu. Morozov, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    In the braided context, we rederive a popular nonsemisimple fusion algebra from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p, 1) logarithmic models of conformal field theory. For this, the category of Yetter-Drinfeld modules is to be regarded as an entwined category (i.e., a category with monodromy but not with braiding). Content Type Journal Article Pages 1329-1358 DOI 10.1007/s11232-012-0118-2 Authors A. M. Semikhatov, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 173 Journal Issue Volume 173, Number 1

Description:    We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A 1 , A 2 , and A 3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice. Content Type Journal Article Pages 1097-1108 DOI 10.1007/s11232-012-0098-2 Authors R. Hernández Heredero, Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, Escuela Universitaria de Ingeniería Técnica de Telecomunicación, Madrid, Spain D. Levi, Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Rome, Italy C. Scimiterna, Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Rome, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We study integrable cutoff constraints for a semidiscrete Toda lattice. We construct a Lax representation for a semidiscrete analogue of lattices corresponding to simple Lie algebras of the C series. We introduce nonlocal variables in terms of which the symmetries of the infinite semidiscrete lattice can be expressed, and we classify cutoff constraints of a certain form compatible with the symmetries of the infinite lattice. Content Type Journal Article Pages 1217-1231 DOI 10.1007/s11232-012-0109-3 Authors S. V. Smirnov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We consider a model initial boundary value problem for the heat equation with double nonlinearity. We use a modified Levin method to prove the solution blowup. Content Type Journal Article Pages 1173-1176 DOI 10.1007/s11232-012-0105-7 Authors M. O. Korpusov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We consider the Boltzmann equation in the framework of a nonlinear model for problems of the gas flow in a half-space (the Kramers problem). We prove the existence of a positive bounded solution and find the limit of this solution at infinity. We show that taking the nonlinear dependence of the collision integral on the distribution function into account leads to an asymptotically new solution of the initial equation. To illustrate the result, we present examples of functions describing the nonlinearity of the collision integral. Content Type Journal Article Pages 1315-1320 DOI 10.1007/s11232-012-0116-4 Authors A. Kh. Khachatryan, Armenian State Agrarian University, Yerevan, Armenia Kh. A. Khachatryan, Institute of Mathematics, Armenian National Academy of Sciences, Yerevan, Armenia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    In a new functional integral approach proposed for the model, we find the regime with a deformed integration measure in which the standard integral is replaced with the Jackson integral. We indicate the relation to a p-adic functional integral. For the magnetic and electronic subsystems in the effective functional that results from the operator formulation of the Hubbard model, we find the two-parametric quantum derivative resulting in the appearance of the quantum SU rq (2) group. We establish the relation to the one-parametric quantum derivative and to the standard derivative. Content Type Journal Article Pages 1300-1314 DOI 10.1007/s11232-012-0115-5 Authors V. M. Zharkov, Institute for Natural Sciences, Perm State University, Perm, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We investigate the Dirac monopole on a three-dimensional torus as a solution of the Bogomolny equations with nontrivial boundary conditions. We show that a suitable analytic continuation of the obtained solution is a three-dimensional generalization of the Kronecker series, satisfies the corresponding functional equation, and is invariant under modular transformations. Content Type Journal Article Pages 1232-1242 DOI 10.1007/s11232-012-0110-x Authors K. M. Bulycheva, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We consider the problem of epitaxial graphene formed on a dimensionally quantized film. We give a microscopic derivation of the quantum kinetic equations for the system “graphene + dimensionally quantized film.” Based on the obtained equations, we investigate the features of electron states of the system under consideration and obtain analytic expressions for the transferred charge in this system. Content Type Journal Article Pages 1278-1288 DOI 10.1007/s11232-012-0113-7 Authors Z. Z. Alisultanov, Prokhorov General Physics Institute, RAS, Moscow, Russia R. P. Meilanov, Institute for Geothermal Problems, Daghestan Science Center, RAS, Makhachkala, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We use number-theoretical methods to study the problem of particle Bose-condensation to zero energy. The parastatistical correction to the Bose-Einstein distribution establishes a relation between the quantum mechanical and statistical definitions of the Bose gas and permits correctly defining the condensation point as a gap in the spectrum in the one-dimensional case, proving the existence of the Bose condensate in the two-dimensional case, and treating the negative pressure in the classical theory of liquids as the pressure of nanopores (holes). Content Type Journal Article Pages 1289-1299 DOI 10.1007/s11232-012-0114-6 Authors V. P. Maslov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established. Content Type Journal Article Pages 1243-1262 DOI 10.1007/s11232-012-0111-9 Authors V. I. Klyatskin, Obukhov Institute for Atmospheric Physics, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We study the stability of planar soliton solutions of equations describing the dynamics of an infinite inextensible unshearable rod under three-dimensional spatial perturbations. As a result of linearization about the soliton solution, we obtain an inhomogeneous scalar equation. This equation leads to a generalized eigenvalue problem. To establish the instability, we must verify the existence of an unstable eigenvalue (an eigenvalue with a positive real part). The corresponding proof of the instability is done using a local construction of the Evans function depending only on the spectral parameter. This function is analytic in the right half of the complex plane and has at least one zero on the positive real axis coinciding with an unstable eigenvalue of the generalized spectral problem. Content Type Journal Article Pages 1206-1216 DOI 10.1007/s11232-012-0108-4 Authors A. T. Il’ichev, Steklov Mathematical Institute, RAS, Moscow, Russia V. Ja. Tomashpolskii, Bauman Moscow State Technical University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We study the quantum analogues of tops on the Lie algebras so (4) and e (3) represented by differential operators. Content Type Journal Article Pages 1187-1205 DOI 10.1007/s11232-012-0107-5 Authors V. E. Adler, Landau Institute for Theoretical Physics, RAS, Moscow, Russia V. G. Marikhin, Landau Institute for Theoretical Physics, RAS, Moscow, Russia A. B. Shabat, Landau Institute for Theoretical Physics, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We discuss the concept of natural geometry for a physical field. We show that using this concept to solve problems of nonlinear electrodynamics allows simply studying basic effects of nonlinear electrodynamics arising when weak electromagnetic waves propagate in external electromagnetic fields. Content Type Journal Article Pages 1321-1327 DOI 10.1007/s11232-012-0117-3 Authors V. I. Denisov, Lomonosov Moscow State University, Moscow, Russia I. P. Denisova, Tsiolkovskii Russian State Technological University, Moscow, Russia V. A. Sokolov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    In topological terms, we compute the spectral flow of an arbitrary family of self-adjoint Dirac-type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by an automorphism of the bundle in which the operators act. We use this result to study conditions for the existence of a nonzero spectral flow of a family of self-adjoint Dirac-type operators with local boundary conditions in a two-dimensional domain with a nontrivial topology and discuss possible physical realizations of a nonzero spectral flow. Content Type Journal Article Pages 1263-1277 DOI 10.1007/s11232-012-0112-8 Authors M. I. Katsnelson, Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen, The Netherlands V. E. Nazaikinskii, Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We consider a class of random connected graphs with random vertices and random edges in which the randomness of the vertices is determined by a continuous probability distribution and the randomness of the edges is determined by a connection function. We derive a strong law of large numbers on the total lengths of all random edges for a random biased connected graph that is a generalization of a directed k-nearest-neighbor graph. Content Type Journal Article Pages 1177-1186 DOI 10.1007/s11232-012-0106-6 Authors Zhonghao Xu, School of Finance and Statistics, East China Normal University, Shanghai, China Y. Higuchi, Department of Mathematics, Kobe University, Kobe, Japan Chunhua Hu, School of Applied Mathematics, Beijing Normal University, Zhuhai, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 3

Description:    We discuss some interesting aspects of the wave breaking in localized solutions of the dispersionless Kadomtsev-Petviashvili equation, an integrable partial differential equation describing the propagation of weakly nonlinear, quasi-one-dimensional waves in 2+1 dimensions, which arise in several physical contexts such as acoustics, plasma physics, and hydrodynamics. For this, we use an inverse spectral transform for multidimensional vector fields that we recently developed and, in particular, the associated inverse problem, a nonlinear Riemann-Hilbert problem on the real axis. In particular, we discuss how the derivative of the solution blows up at the first breaking point in any direction of the plane (x, y) except in the transverse breaking direction and how the solution becomes three-valued in a compact region of the plane (x, y) after the wave breaking. Content Type Journal Article Pages 1118-1126 DOI 10.1007/s11232-012-0100-z Authors S. V. Manakov, Landau Institute for Theoretical Physics, Moscow, Russia P. M. Santini, Dipartimento di Fisica, Università di Roma “La Sapienza,” Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Rome, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We study special solutions of the Painlevé II (PII) equation called tronquée solutions, i.e., those having no poles along one or more critical rays in the complex plane. They are parameterized by special monodromy data of the Lax pair equations. The manifold of the monodromy data for a general solution is a twodimensional complex manifold with one- and zero-dimensional singularities, which arise because there is no global parameterization of the manifold. We show that these and only these singularities (together with zeros of the parameterization) are related to the tronquée solutions of the PII equation. As an illustration, we consider the known Hastings-McLeod and Ablowitz-Segur solutions and some other solutions to show that they belong to the class of tronquée solutions and correspond to one or another type of singularity of the monodromy data. Content Type Journal Article Pages 1136-1146 DOI 10.1007/s11232-012-0102-x Authors V. Yu. Novokshenov, Institute of Mathematics, RAS, Ufa, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We consider the heat operator with a general multisoliton potential and derive its extended resolvent depending on a parameter q ∈ ℝ 2 . We show that it is bounded in all variables and find its singularities in q . We introduce the Green’s functions and study their properties in detail. Content Type Journal Article Pages 1037-1051 DOI 10.1007/s11232-012-0094-6 Authors M. Boiti, Dipartimento di Fisica, Università del Salento and Sezione INFN, Lecce, Italy F. Pempinelli, Dipartimento di Fisica, Università del Salento and Sezione INFN, Lecce, Italy A. K. Pogrebkov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We propose a mechanical (Hamiltonian) interpretation of the so-called spectrality property introduced by Sklyanin and Kuznetsov in the context of Bäcklund transformations (BTs) for finite-dimensional integrable systems. This property turns out to be deeply connected with the Hamilton-Jacobi separation of variables and can lead to the explicit integration of the corresponding model using the BTs. We show that once such a construction is given, we can interpret the Baxter Q-operator defining the quantum BTs as the Green’s function or the propagator of the time-dependent Schrödinger equation for an interpolating Hamiltonian. Content Type Journal Article Pages 1160-1171 DOI 10.1007/s11232-012-0104-8 Authors O. Ragnisco, Dipartimento di Fisica, Università di Roma Tre, Rome, Italy F. Zullo, School of Mathematics, Statistics, and Actuarial Science, University of Kent, Canterbury, Kent, UK Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    The starting point is an N×N matrix, U ≡ U(ℓ), evolving in the discrete-time independent variable ℓ = 0, 1, 2, ... according to a solvable matrix evolution equation. One then focuses on the evolution of its N eigenvalues z n (ℓ). This evolution generally also involves N(N−1) additional variables. In some cases via a compatible ansatz these additional variables can be expressed in terms of the N variables z n (ℓ). Thereby one obtains a system of discrete-time evolution equations involving only the N dependent variables z n (ℓ), which is often interpretable as a discrete-time many-body problem. Various peculiarities of this approach are investigated, including the possibility to manufacture nontrivial isochronous models (all solutions of which are periodic with the same period). These properties are illustrated via specific examples. In the process novel discrete-time many-body problems are exhibited. Content Type Journal Article Pages 1052-1072 DOI 10.1007/s11232-012-0095-5 Authors F. Calogero, Physics Department, University of Rome “La Sapienza”, Rome, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We derive an extended nonlinear dispersion for envelope soliton equations and also find generalized equations of the nonlinear Schrödinger (NLS) type associated with this dispersion. We show that space dilatations imply hyperbolic rotation of the pair of dual equations, the NLS and resonant NLS (RNLS) equations. For the RNLS equation, in addition to the Madelung fluid representation, we find an alternative non-Madelung fluid system in the form of a Broer-Kaup system. Using the bilinear form for the RNLS equation, we construct the soliton resonances for the Broer-Kaup system and find the corresponding integrals of motion and existence conditions for the soliton resonance and also a geometric interpretation in terms of a pseudo-Riemannian surface of constant curvature. This approach can be extended to construct a resonance version and the corresponding Broer-Kaup-type representation for any envelope soliton equation. As an example, we derive a new modified Broer-Kaup system from the modified NLS equation. Content Type Journal Article Pages 1147-1159 DOI 10.1007/s11232-012-0103-9 Authors O. K. Pashaev, Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 172 Journal Issue Volume 172, Number 2

Description:    We introduce a dual map from the special class A of quantum observables â to a special class of generalized functions a(X, ϕ). The class A includes all symmetrized polynomials in the canonical variables and . Content Type Journal Article Pages 832-838 DOI 10.1007/s11232-012-0078-6 Authors G. G. Amosov, Steklov Mathematical Institute, RAS, Moscow, Russia Ya. A. Korennoy, Lebedev Physical Institute, RAS, Moscow, Russia V. I. Man’ko, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider the Boltzmann equation for the hard-sphere model. We construct an explicit approximate solution of this equation in the form of a continuum distribution in the case of global Maxwellians. We obtain some sufficient conditions for attaining the minimum of the uniform-integral mismatch between the sides of the equation. Content Type Journal Article Pages 839-847 DOI 10.1007/s11232-012-0079-5 Authors V. D. Gordevskyy, Karazin Kharkov National University, Kharkov, Ukraine E. S. Sazonova, Karazin Kharkov National University, Kharkov, Ukraine Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider a two-particle discrete Schrödinger operator corresponding to a system of two identical particles on a lattice interacting via an attractive pairwise zero-range potential. We show that there is a unique eigenvalue below the bottom of the essential spectrum for all values of the coupling constant and two-particle quasimomentum. We obtain a convergent expansion for the eigenvalue. Content Type Journal Article Pages 800-811 DOI 10.1007/s11232-012-0076-8 Authors S. N. Lakaev, Samarkand Branch, Uzbekistan Academy of Sciences, Samarkand, Uzbekistan A. M. Khalkhuzhaev, Samarkand Branch, Uzbekistan Academy of Sciences, Samarkand, Uzbekistan Sh. S. Lakaev, Samarkand State University, Samarkand, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider the Dirichlet problem for a nonlinear system of equations, continuing our study of nonlinear hyperbolic equations and systems of equations with an arbitrarily large positive energy. We use a modified Levine method to prove the blow-up. Content Type Journal Article Pages 725-738 DOI 10.1007/s11232-012-0070-1 Authors M. O. Korpusov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We show that the mathematical formalisms of general relativity and of quantum mechanics can be reconciled based on an algebraic approach. In this case, gravity does not need to be quantized. Content Type Journal Article Pages 848-861 DOI 10.1007/s11232-012-0080-z Authors D. A. Slavnov, Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We investigate the influence of demagnetizing fields on the conditions for the appearance of magnetic inhomogeneities of the type of 0 -degree domain walls in thin ferromagnetic films and on their structure theoretically. We obtain expressions for demagnetizing fields generated by samples of a given geometry in the thin-film approximation and find the magnetization distributions for non-Bloch-type inhomogeneities and their stability region. Content Type Journal Article Pages 862-869 DOI 10.1007/s11232-012-0081-y Authors E. B. Magadeev, Bashkir State University, Ufa, Russia R. M. Vakhitov, Bashkir State University, Ufa, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We introduce a way to represent pairs (E,∇), where E is a bundle on a Riemann surface and ∇ is a logarithmic connection in E, based on a representation of the surface as the quotient of the exterior of the unit disc. In this representation, we write the local isomonodromic deformation conditions for the pairs (E,∇). These conditions are written as a modified Schlesinger system on a Riemann sphere (reduced to the ordinary Schlesinger system in the typical case) supplemented by a certain system of linear equations. Content Type Journal Article Pages 739-753 DOI 10.1007/s11232-012-0071-0 Authors D. V. Artamonov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider a system of three arbitrary quantum particles on a one-dimensional lattice interacting pairwise via attractive contact potentials. We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum in the case where the masses of two particles are finite. We show that the discrete spectrum of the Schrödinger operator is infinite in the case where the masses of two particles in a three-particle system are infinite. Content Type Journal Article Pages 754-768 DOI 10.1007/s11232-012-0072-z Authors M. É. Muminov, Samarkand State University, Samarkand, Uzbekistan N. M. Aliev, Samarkand State University, Samarkand, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider the Pauli group P q generated by unitary quantum generators X (shift) and Z (clock) acting on vectors of the q-dimensional Hilbert space. It has been found that the number of maximal mutually commuting sets within P q is controlled by the Dedekind psi function ψ(q) and that there exists a specific inequality involving the Euler constant γ ∼ 0.577 that is only satisfied at specific low dimensions q ∈ A = { 2, 3, 4, 5, 6, 8, 10, 12, 18, 30 }. The set A is closely related to the set A∪{ 1, 24 } of integers that are totally Goldbach, i.e., that consist of all primes p 〈 n − 1 with p not dividing n and such that n–p is prime. In the extreme high-dimensional case, at primorial numbers N r , the Hardy-Littlewood function R(q) is introduced for estimating the number of Goldbach pairs, and a new inequality (Theorem 4 ) is established for the equivalence to the Riemann hypothesis in terms of R(N r ). We discuss these number-theoretical properties in the context of the qudit commutation structure. Content Type Journal Article Pages 780-791 DOI 10.1007/s11232-012-0074-x Authors M. Planat, FEMTO-ST Institute, CNRS, Besançon, France F. Anselmi, FEMTO-ST Institute, CNRS, Besançon, France P. Solé, Telecom ParisTech, Paris, France Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We derive analytic formulas for the geometric measure of quantum discord introduced by Dakic, Vedral, and Brukner for pure states and ( 2 × n )-dimensional states and establish a general lower bound for arbitrary states. Content Type Journal Article Pages 870-878 DOI 10.1007/s11232-012-0082-x Authors Shunlong Luo, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China Shuangshuang Fu, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We formulate a method for representing solutions of homogeneous second-order equations in the form of a functional integral or path integral. As an example, we derive solutions of second-order equations with constant coefficients and a linear potential. The method can be used to find general solutions of the stationary Schrödinger equation. We show how to find the spectrum and eigenfunctions of the quantum oscillator equation. We obtain a solution of the stationary Schrödinger equation in the semiclassical approximation, without a singularity at the turning point. In that approximation, we find the coefficient of transmission through a potential barrier. We obtain a representation for the elastic potential scattering amplitude in the form of a functional integral. Content Type Journal Article Pages 812-831 DOI 10.1007/s11232-012-0077-7 Authors G. V. Efimov, Joint Institute for Nuclear Research, Dubna, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We derive and investigate the equation of state for a system with a fractional-power spectrum and also derive an expression for the density of states in such systems. We consider a fractional-differential model of electron-phonon interaction. Content Type Journal Article Pages 769-779 DOI 10.1007/s11232-012-0073-y Authors Z. Z. Alisultanov, Prokhorov General Physics Institute, RAS, Moscow, Russia R. P. Meilanov, Daghestan State University, Makhachkala, Daghestan, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider the question of integrable boundary-value problems in the examples of the two-dimensional Toda chain and Kadomtsev-Petviashvili equation. We discuss the problems that are integrable from the standpoints of two basic definitions of integrability. As a result, we propose a method for constructing a hierarchy of integrable boundary-value problems where the boundaries are cylindric surfaces in the space of three variables. We write explicit formulas describing wide classes of solutions of these boundary-value problems for the two-dimensional Toda chain and Kadomtsev-Petviashvili equation. Content Type Journal Article Pages 792-799 DOI 10.1007/s11232-012-0075-9 Authors V. L. Vereshchagin, Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 3

Description:    We consider the decomposition of the pth tensor power of the module L w 1 over the algebra A n into irreducible modules, ( L w 1 ) Ä p = å v m ( v , p ) L v . This problem occurs, for example, in finding the spectrum of an invariant Hamiltonian of a spin chain with p nodes. To solve the problem, we propose using the Weyl symmetry properties. For constructing the coefficients m(ν, p) as functions of p, we develop an algorithm applicable to powers of an arbitrary module. We explicitly write an expression for the multiplicities m(ν, p) in the decomposition of powers of the first fundamental module of sl(n+ 1 ). Based on the obtained results, we find new properties of systems of orthogonal polynomials (multivariate Chebyshev polynomials). Our algorithm can also be applied to tensor powers of modules of other simple Lie algebras. Content Type Journal Article Pages 666-674 DOI 10.1007/s11232-012-0063-0 Authors P. P. Kulish, St. Petersburg Department of the Steklov Institute for Mathematics, RAS, St. Petersburg, Russia V. D. Lyakhovsky, St. Petersburg State University, St. Petersburg, Russia O. V. Postnova, St. Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    Defects are ubiquitous in nature, for example, in the form of dislocations, shocks, bores, or impurities of various kinds, and their descriptions are an important part of any physical theory. But the following question can be asked. What types of defect are allowed, and what are their properties if maintaining integrability within an integrable field theory in two-dimensional space-time is required? We consider a collection of ideas and questions connected with this problem, including examples of integrable defects and the curiously special roles played by energy-momentum conservation and Bäcklund transformations, solitons scattering on defects, and some interesting effects in the framework of the sine-Gordon model, defects in integrable quantum field theory, and the construction of transmission matrices. In conclusion, we remark on algebraic considerations and future research directions. Content Type Journal Article Pages 655-665 DOI 10.1007/s11232-012-0062-1 Authors E. Corrigan, Department of Mathematics, University of York, York, UK Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We study a limit relation between the elliptic SL(N, ℂ ) top and Toda chains. We show that in the case of the nonautonomous SL( 2, ℂ ) top, whose equations of motion are related to the Painlevé VI equation, it turns out to be possible to modify the previously proposed procedure and in the limit obtain the nonautonomous Toda chain, whose equations of motion are equivalent to a particular case of the Painlevé III equation. We obtain the limit of the Lax pair for the elliptic SL( 2, ℂ ) top, which allows representing the equations of motion of the nonautonomous Toda chain as the equation for isomonodromic deformations. Content Type Journal Article Pages 575-588 DOI 10.1007/s11232-012-0056-z Authors G. A. Aminov, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We construct a “spectral curve” for the generalized Toda system, which allows efficiently finding its quantization. In turn, the quantization is realized using the technique of the quantum characteristic polynomial for the Gaudin system and an appropriate Alder-Kostant-Symes reduction. We also discuss some relations of this result to the recent consideration of the Drinfeld Zastava space, the monopole space, and corresponding symmetries of the Borel Yangian. Content Type Journal Article Pages 691-699 DOI 10.1007/s11232-012-0066-x Authors D. V. Talalaev, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We show that exotic Lagrangian tori constructed by Chekanov and Schlenk can be obtained for a large class of toric manifolds. For this, we translate their original construction into the language of pseudotoric structures. As an example, we construct exotic Lagrangian tori on a del Pezzo surface of degree six. Content Type Journal Article Pages 700-703 DOI 10.1007/s11232-012-0067-9 Authors N. A. Tyurin, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We consider the scaling limit of an elliptic top. This limit is a combination of a scaling of the elliptic top variables, an infinite shift of the spectral parameter, and the trigonometric limit. We give general necessary constraints on the scaling of the variables and examples of such a degeneracy. A certain subclass of limit systems is integrable in the Liouville sense, which can also be shown directly. Content Type Journal Article Pages 589-599 DOI 10.1007/s11232-012-0057-y Authors S. B. Arthamonov, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We present a simple derivation of the spectra of the action variables of the quantized compactified Ruijsenaars-Schneider system. We obtain the spectra by combining Kähler quantization with the identification of the classical action variables as a standard toric moment map on a complex projective space. The result is consistent with the Schrödinger quantization of the system previously developed by van Diejen and Vinet. Content Type Journal Article Pages 704-714 DOI 10.1007/s11232-012-0068-8 Authors L. Fehér, Department of Theoretical Physics, Wigner KFKI RMKI, Budapest, Hungary C. Klimčík, Institut de Mathématiques de Luminy, Marseille, France Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We consider the gravimagnetization of the N= 2 supersymmetric vacuum in the presence of the Ω -deformation. We argue that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean space ℝ 4 . We conjecture the possible role of the dyonic instantons as the microscopic angular momentum carriers that could yield a spontaneous vacuum gravimagnetization. We interpret the dyonic instanton as an analogue of the Euclidean bounce in ℝ 4 . Such a bounce is related to the Schwinger pair production. We also briefly discuss the induced angular momentum in ℝ 4 in the dual Liouville formulation of the SU (2) theory in terms of the hypothesis of the Alday-Gaiotto-Tachikawa correspondence. Content Type Journal Article Pages 616-628 DOI 10.1007/s11232-012-0059-9 Authors A. S. Gorsky, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We derive generalized multiflow hydrodynamic reductions of the nonlocal kinetic equation for a soliton gas and investigate their structure. These reductions not only provide further insight into the properties of the new kinetic equation but also could prove to be representatives of a novel class of integrable systems of hydrodynamic type beyond the conventional semi-Hamiltonian framework. Content Type Journal Article Pages 675-682 DOI 10.1007/s11232-012-0064-z Authors M. V. Pavlov, Lebedev Physical Institute, RAS, Moscow, Russia V. B. Taranov, Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kiev, Ukraine G. A. El, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, UK Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We address the problem of calculating correlation functions in the six-vertex model with domain wall boundary conditions by considering a particular nonlocal correlation function, called the row configuration probability. This correlation function can be used as a building block for computing various (both local and nonlocal) correlation functions in the model. We calculate the row configuration probability using the quantum inverse scattering method, giving the final result in terms of multiple integrals. We also discuss the relation to the emptiness formation probability, another nonlocal correlation function, which was previously computed using similar methods. Content Type Journal Article Pages 641-654 DOI 10.1007/s11232-012-0061-2 Authors F. Colomo, INFN, Sezione di Firenze, Firenze, Italy A. G. Pronko, St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    We consider a third-order generalized Monge-Ampère equation u yyy − u xxy 2 + u xxx u xyy = 0 , which is closely related to the associativity equation in two-dimensional topological field theory. We describe all integrable structures related to it: Hamiltonian, symplectic, and also recursion operators. We construct infinite hierarchies of symmetries and conservation laws. Content Type Journal Article Pages 600-615 DOI 10.1007/s11232-012-0058-x Authors A. M. Verbovetsky, Independent University of Moscow, Moscow, Russia R. Vitolo, Department of Mathematics “E. De Giorgi”, University of Salento, Lecce, Italy P. Kersten, Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands I. S. Krasil’shchik, Independent University of Moscow, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    Nonparallel boundary magnetic fields can induce a longitudinal (spin) current in a quantum spin chain. We use functional approaches to formulate the spectral problem for the spin- 1/2 Heisenberg model subject to a class of integrable boundary conditions in terms of an infinite hierarchy of nonlinear integral equations. From these equations, we compute finite-size corrections to the ground-state energy of the antiferromagnetic chain and the induced spin current for a certain range of boundary parameters. Content Type Journal Article Pages 715-724 DOI 10.1007/s11232-012-0069-7 Authors H. Frahm, Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, Germany J. H. Grelik, Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, Germany A. Seel, Institut für Theoretische Elektrotechnik und Photonik, Universität Siegen, Siegen, Germany Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description:    In the matrix density formalism for a charged spinor particle located in a constant uniform magnetic field, we develop a technique for calculating the reaction rate and the four-momentum carried away from a plasma by a neutrino in one-vertex neutrino processes. Using this technique, we reproduce results for the luminosity in processes of neutrino synchrotron emission by electrons (positrons) and of electron-positron annihilation producing the neutrino pair. Content Type Journal Article Pages 354-375 DOI 10.1007/s11232-012-0035-4 Authors A. A. Gvozdev, Demidov Yaroslavl State University, Yaroslavl, Russia E. V. Osokina, Demidov Yaroslavl State University, Yaroslavl, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We study the position of the essential spectrum of a three-body Schrödinger operator H. We evaluate the lower boundary of the essential spectrum of H and prove that the number of eigenvalues located below the lower edge of the essential spectrum in the H model is finite. Content Type Journal Article Pages 341-353 DOI 10.1007/s11232-012-0034-5 Authors Yu. Kh. Eshkabilov, Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan R. R. Kucharov, Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We consider the two-particle discrete Schrödinger operator H μ (K) corresponding to a system of two arbitrary particles on a d-dimensional lattice ℤ d , d ≥ 3, interacting via a pair contact repulsive potential with a coupling constant μ 〉 0 ( K Î \mathbb T d is the quasimomentum of two particles). We find that the upper (right) edge of the essential spectrum can be either a virtual level (for d = 3, 4 ) or an eigenvalue (for d ≥ 5 ) of H μ (K). We show that there exists a unique eigenvalue located to the right of the essential spectrum, depending on the coupling constant μ and the two-particle quasimomentum K. We prove the analyticity of the corresponding eigenstate and the analyticity of the eigenvalue and the eigenstate as functions of the quasimomentum K Î \mathbb T d in the domain of their existence. Content Type Journal Article Pages 326-340 DOI 10.1007/s11232-012-0033-6 Authors S. N. Lakaev, Samarkand State University, Samarkand, Uzbekistan S. S. Ulashov, Samarkand State University, Samarkand, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We calculate cohomologies of the Schwartz algebras D and S, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras E/D and M/S (E andMare also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics. Content Type Journal Article Pages 263-273 DOI 10.1007/s11232-012-0028-3 Authors V. V. Zharinov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We consider the screening of an external magnetic field in which a superconducting ellipsoid is inserted and a change in the velocity distribution in an ideal liquid flowing around an ellipsoid inserted in it. In both cases, the solution is given by a harmonic vector field parallel to the surface near the ellipsoid. Content Type Journal Article Pages 315-325 DOI 10.1007/s11232-012-0032-7 Authors A. O. Savchenko, Institute for Computational Mathematics and Mathematical Geophysics, Siberian Branch, RAS, Novosibirsk, Russia O. Ya. Savchenko, Novosibirsk State University, Novosibirsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We construct a family of perfect gases depending on the critical value of the compressibility factor Z for pure gases. We show that the critical indices of actual simple liquids, like many other thermodynamic effects, easily and naturally follow from the concept of Wiener quantization of modern thermodynamics. Content Type Journal Article Pages 384-393 DOI 10.1007/s11232-012-0037-2 Authors V. P. Maslov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We prove that Hilbert’s causality principle and the equations of general relativity exclude the possibility that a black hole can form. Content Type Journal Article Pages 413-419 DOI 10.1007/s11232-012-0040-7 Authors A. A. Logunov, Institute for High Energy Physics, Protvino, Russia M. A. Mestvirishvili, Institute for High Energy Physics, Protvino, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We consider a stationary discrete model of the Boltzmann equation for four velocities (the Broadwell model). We obtain new exact automodel solutions of the model corresponding to an incompressible and a compressible gas. We show that one class of solutions satisfies the problem of gas evaporation and condensation on the boundary of a disk and external space. The system turns out to be strongly nonequilibrium, and continuous medium equations are not applicable to it. Content Type Journal Article Pages 406-412 DOI 10.1007/s11232-012-0039-0 Authors O. V. Ilyin, Dorodnitsyn Computation Center, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    We consider the initial boundary value problem for the well-known three-dimensional Rosenau-Burgers equation in the cylinder (0, L ) Ä \mathbb S (where \mathbb S Ì \mathbb R 2 ) for some boundary conditions. Using the test-function method, we obtain the result on the blowup of solutions of this initial boundary value problem during a finite time. This is one of the first results in the “blowup” direction for this equation. Content Type Journal Article Pages 280-286 DOI 10.1007/s11232-012-0030-9 Authors M. O. Korpusov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    Using a multidimensional super Riemann theta function, we propose two key theorems for explicitly constructing multiperiodic super Riemann theta function periodic wave solutions of supersymmetric equations in the superspace ℝ Λ N+ 1 ,M , which is a lucid and direct generalization of the super-Hirota-Riemann method. Once a supersymmetric equation is written in a bilinear form, its super Riemann theta function periodic wave solutions can be directly obtained by using our two theorems. As an application, we present a supersymmetric Korteweg-de Vries-Burgers equation. We study the limit procedure in detail and rigorously establish the asymptotic behavior of the multiperiodic waves and the relations between periodic wave solutions and soliton solutions. Moreover, we find that in contrast to the purely bosonic case, an interesting phenomenon occurs among the super Riemann theta function periodic waves in the presence of the Grassmann variable. The super Riemann theta function periodic waves are symmetric about the band but collapse along with the band. Furthermore, the results can be extended to the case N 〉 2 ; here, we only consider an existence condition for an N-periodic wave solution of a general supersymmetric equation. Content Type Journal Article Pages 287-314 DOI 10.1007/s11232-012-0031-8 Authors Shou-fu Tian, School of Mathematical Sciences, Dalian University of Technology, Dalian, China Hong-qing Zhang, School of Mathematical Sciences, Dalian University of Technology, Dalian, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 170 Journal Issue Volume 170, Number 3

Description:    A new integrable (indeed, solvable) model of goldfish type is identified, and some of its properties are discussed. Its Newtonian equations of motion read as follows: × × z   n   = \frac × z   2 n   z n + c 1 \frac × z   n   z n + c 2 × z   n   + c 2 c 3 z n + c 1 c 2 + N å m = 1, m ¹ n   \frac( [( z )\dot] n + c 3 z

Description:    We briefly review a recursive construction of ħ-dependent solutions of the Kadomtsev-Petviashvili hierarchy. We give recurrence relations for the coefficients X n of an ħ-expansion of the operator X = X 0 + ħX 1 + ħ 2 X 2 + ... for which the dressing operator W is expressed in the exponential form W = e X/ħ . The wave function Ψ associated with W turns out to have the WKB (Wentzel-Kramers-Brillouin) form Ψ = e S/kh , and the coefficients S n of the ħ-expansion S = S 0 + ħS 1 + ħ 2 S 2 + ... are also determined by a set of recurrence relations. We use this WKB form to show that the associated tau function has an ħ-expansion of the form log τ = ħ − 2 F 0 + ħ − 1 F 1 + F 2 + .... Content Type Journal Article Pages 683-690 DOI 10.1007/s11232-012-0065-y Authors K. Takasaki, Graduate School of Human and Environmental Studies, Kyoto University, Yoshida, Sakyo, Kyoto, Japan T. Takebe, Faculty of Mathematics, Higher School of Economics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 2

Description: Abstact   We consider commuting differential operators with two independent variables of general form and obtain general necessary commutativity conditions for low-order operators. We show that these conditions allow classifying commuting pairs of operators whose coefficients are linear functions of the independent variables. Content Type Journal Article Pages 435-441 DOI 10.1007/s11232-012-0042-5 Authors R. A. Gabiev, Aliev Karachai-Cherkess State University, Karachaevsk, Russia A. B. Shabat, Aliev Karachai-Cherkess State University, Karachaevsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 1

Description:    We study the dynamics of systems consisting of interacting two-level atoms and a field (microcavities). Such systems include the Jaynes-Cummings model. We formulate the problem and present a short history of it, derive a generalized kinetic equation for the system, find its solution, and show that this model allows describing photon emission and absorption. Content Type Journal Article Pages 523-530 DOI 10.1007/s11232-012-0050-5 Authors N. N. Bogolyubov Jr., Steklov Mathematical Institute, RAS, Moscow, Russia M. Yu. Rasulova, Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Ulugbek, Tashkent, Uzbekistan I. A. Tishabaev, Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Ulugbek, Tashkent, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 1

Description:    We develop a semiclassical approximation of the Dirac equation in a central field with a Coulomb asymptotic behavior. We obtain relativistic semiclassical scattering phases, energy levels of hydrogen-like ions, and a semiclassical expression for the multiplicative constant in the asymptotic expansion of the wave function of the valence electron in a relativistic multiply charged ion, which plays an important role in quantum defect theory. Content Type Journal Article Pages 478-489 DOI 10.1007/s11232-012-0046-1 Authors B. A. Zon, Voronezh State University, Voronezh, Russia A. S. Kornev, Voronezh State University, Voronezh, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 1

Description:    We calculate the Anderson criterion and the spectral dependence of the degree of localization in the first nonvanishing approximation with respect to disorder for one-dimensional diagonally disordered models with a site energy distribution function that has no finite even moments higher than the zeroth. For this class of models (for which the usual perturbation theory is inapplicable), we show that the perturbation theory can be consistently constructed for the joint statistics of advanced and retarded Green’s functions. Calculations for the Lloyd model show that the Anderson criterion in this case is a linear (not quadratic as usual) function of the disorder degree. We illustrate the calculations with computer experiments. Content Type Journal Article Pages 531-540 DOI 10.1007/s11232-012-0051-4 Authors G. G. Kozlov, Fock Institute of Physics, St. Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 1

Description:    It is known that a self-adjoint, time-independent Hamiltonian can be defined for the quantum damped harmonic oscillator. We show that the two vacuums naturally associated with this operator seem to be non-square-integrable when it is expressed in terms of pseudo-bosonic lowering and raising operators. This fact is interpreted as the evidence of a dissipation effect of the classical oscillator on a purely quantum level. Content Type Journal Article Pages 497-504 DOI 10.1007/s11232-012-0048-z Authors F. Bagarello, DIEETCAM, Università di Palermo, Palermo, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 171 Journal Issue Volume 171, Number 1