On classification of soliton solutions of multicomponent nonlinear evolution equations

    Authors

    V. S. Gerdjikov; D. J. Kaup; N. A. Kostov;T. I. Valchev

    Comments

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    Abbreviated Journal Title

    J. Phys. A-Math. Theor.

    Keywords

    SIMPLE LIE-ALGEBRAS; NERVE AXON EQUATIONS; RESONANT INTERACTION; REDUCTION PROBLEM; SPACE-TIME; SCATTERING; MODELS; SYSTEM; OPERATOR; MEDIA; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    We consider several ways of how one could classify the various types of soliton solutions related to multicomponent nonlinear evolution equations which are solvable by the inverse scattering method for the generalized Zakharov-Shabat system related to a simple Lie algebra g. In doing so we make use of the fundamental analytic solutions, the Zakharov-Shabat dressing procedure, the reduction technique and other tools characteristic for that method. The multicomponent solitons are characterized by several important factors: the subalgebras of g and the way these subalgebras are embedded in g, the dimension of the corresponding eigensubspaces of the Lax operator L, as well as by additional constraints imposed by reductions.

    Journal Title

    Journal of Physics a-Mathematical and Theoretical

    Volume

    41

    Issue/Number

    31

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    36

    WOS Identifier

    WOS:000257564900020

    ISSN

    1751-8113

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