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  • 1
    Electronic Resource
    Electronic Resource
    Bäcklund transformation and its superposition principle of a Blaszak–Marciniak four-field lattice (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6071-6086 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A four-field lattice furnished by Blaszak and Marciniak is transformed into bilinear form upon introducing two auxiliary independent variables. A Bäcklund transformation in bilinear form is found for the lattice and the corresponding nonlinear superposition formula is rigorously established. As a consequence, soliton solutions to the lattice are derived. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533071
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  • 2
    Electronic Resource
    Electronic Resource
    Comment on "Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation" [J. Math. Phys. 36, 3492 (1995)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3685-3690 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two remarks on an inverse operator of a differential operator ∂x and on symmetries of two kinds of differential equations Δ(u)=0 and ∂xΔ(u)=0 are pointed out and then a few of remarks about the paper "Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation" [Y. Lou and J. P. Weng, J. Math. Phys. 36, 3492 (1995)] are presented. It is in particular shown that if we consider ∂x−1 to be a linear and right inverse operator of ∂x, the vector fields σnu(f ) proposed in the above paper are not certain to be symmetries of the Jimbo–Miwa–Kadomtsev–Petviashvili system under consideration. Moreover the commutators of a generalized W∞ algebra established among these vector fields do not always hold. Therefore the vector fields σnu(f ) do not provide an example of application of the formal series ansatz in the above paper. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532916
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  • 3
    Electronic Resource
    Electronic Resource
    Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2400-2418 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows (λt=λl, l≥0) from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532872
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  • 4
    Electronic Resource
    Electronic Resource
    Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2464-2476 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method of constructing Lax representations for isospectral and nonisospectral hierarchies of evolution equations is proposed. It is shown that under some simple but essential conditions, the corresponding Lax operators may constitute infinite-dimensional Lie algebras with respect to the binary operation (large-closed-square)⋅,⋅(large-closed-square) given in this paper. Furthermore, the detailed analyses for the KdV couple, the AKNS couple, and a new couple of isospectral and nonisospectral hierarchies of integrable equations are presented as examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529616
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  • 5
    Electronic Resource
    Electronic Resource
    A bi-Hamiltonian formulation for triangular systems by perturbations (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1408-1421 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A bi-Hamiltonian formulation is proposed for triangular systems resulting from perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through our formulation, four examples of triangular systems are exhibited, which also show that bi-Hamiltonian systems in both lower dimensions and higher dimensions are many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian systems and illustrate that multiscale perturbations can lead to higher-dimensional bi-Hamiltonian systems. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1432775
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  • 6
    Electronic Resource
    Electronic Resource
    Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4345-4382 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Binary symmetry constraints of the N-wave interaction equations in 1+1 and 2+1 dimensions are proposed to reduce the N-wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally independent system of polynomial functions is generated from an arbitrary order square matrix Lax operator and used to show the Liouville integrability of the constrained flows of the N-wave interaction equations. The constraints on the potentials resulting from the symmetry constraints give rise to involutive solutions to the N-wave interaction equations, and thus the integrability by quadratures are shown for the N-wave interaction equations by the constrained flows. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1388898
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  • 7
    Electronic Resource
    Electronic Resource
    A coupled AKNS–Kaup–Newell soliton hierarchy (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4419-4428 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A coupled AKNS–Kaup–Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS–Kaup–Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup–Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532976
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  • 8
    Electronic Resource
    Electronic Resource
    A Note on Symmetries and Generalized W∞ Algebra of the Modified KP Equation (1997)
    Springer
    Letters in mathematical physics 41 (1997), S. 237-241 
    Details
    ISSN: 1573-0530
    Keywords: time dependent symmetry ; the modified KP equation ; symmetry algebra.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Some remarks on the paper ‘Symmetries and generalized W∞ algebra of the modified KP equation’ (S. Y. Lou and G. J. Ni, Lett. Math. Phys. 34 (1995), 327–331) are given. It is pointed out that if we consider the inverse operator of a differential operator to be a linear operator, the vector fields σnv(f) defined in the above Letter are not certain to be symmetries of the modified KP equation under consideration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007333109170
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  • 9
    Electronic Resource
    Electronic Resource
    Lax representations and zero-curvature representations by the Kronecker product (1997)
    Springer
    International journal of theoretical physics 36 (1997), S. 697-704 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that the Kronecker product can be applied to construct not only new Lax representations, but also new zero-curvature representations of integrable models. A characteristic difference between continuous and discrete zero-curvature equations is pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02435889
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  • 10
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    Comment on “Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation” [J. Math. Phys.36, 3492 (1995)] (1999)
    American Institute of Physics
    Details
    Publication Date: 1999-07-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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