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  • American Institute of Physics (AIP)  (5)
Collection
Publisher
Years
  • 1
    Electronic Resource
    Electronic Resource
    Group analysis of the three-wave resonant system in (2+1) dimensions (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2623-2628 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The three-wave resonant interaction equations (2D-3WR) in two spatial and one temporal dimension within a group framework are analyzed. The symmetry algebra of this system, which turns out to be an infinite-dimensional Lie algebra whose subalgebra is of the Kac–Moody type, is found. The one- and two-dimensional symmetry subalgebras are classified and the corresponding reduction equations are obtained. From these the new invariant and the partially invariant solutions of the original 2D-3WR equations are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527280
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Gauge equivalence theory of the noncompact Ishimori model and the Davey–Stewartson equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1515-1522 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The gauge equivalence between a noncompact version of the Ishimori spin model and the Davey–Stewartson equation is established. Explicit relationships connecting the corresponding two sets of fields involved in these systems are obtained via any pair of complex functions satisfying an equation of the Schrödinger type for a free particle. Using these formulas, two examples of classes of nontrivial exact singular solutions to the Davey–Stewartson equation are given. One of them is of the closed stringlike type, while the other is doubly periodic and is expressed in terms of Riemann theta functions. The role played by the symmetry group associated with the gauge equivalent equations under consideration is also clarified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529676
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  • 3
    Electronic Resource
    Electronic Resource
    Topological field theories and integrable models (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 1397-1412 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the classical non-Abelian pure Chern–Simons action is related to nonrelativistic models in (2+1) dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern–Simons fields, associated with the isotropy subgroup of the considered symmetric space. Thus a relation between the Chern–Simons theory and the Davey–Stewartson hierarchy is established in a natural way. The Bäcklund transformations are interpreted in terms of Chern–Simons constraints. Moreover, certain nonintegrable Heisenberg models can be embedded into the pure Chern–Simons theory. The main classical and quantum properties of these systems are discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531901
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  • 4
    Electronic Resource
    Electronic Resource
    On the Painlevé property of nonlinear field equations in 2+1 dimensions: The Davey–Stewartson system (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2666-2671 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: With the purpose of clarifying some aspects of the complete integrability of nonlinear field equations, a singular-point analysis is performed of the Davey–Stewartson system, which can be considered as an extension in 2+1 dimensions of the nonlinear Schrödinger equation. It is found that the system under consideration possesses the Painlevé property and allows a set of Bäcklund transformations obtained by truncating the series expansions of the solutions about the singularity manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528058
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  • 5
    Electronic Resource
    Electronic Resource
    The classical theory of the transverse optical klystron for a nonmonoenergetic beam (1985)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 57 (1985), S. 18-26 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper the classical theory of the transverse optical klystron is presented. The gain is obtained by solving analytically the Vlasov equation which governs the evolution of the electron beam along the undulator magnet. The initial energy distribution of the electron beam is assumed gaussian. Both the small signal and the saturation regime are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.335388
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