Squared eigenfunctions and the perturbation theory for the nondegenerate N x N operator: a general outline

    Authors

    D. J. Kaup;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Phys. A-Math. Theor.

    Keywords

    INVERSE SCATTERING TRANSFORM; RESONANT INTERACTION; NONLINEAR MEDIA; WAVE PACKETS; SOLITONS; EQUATIONS; EVOLUTION; SYSTEMS; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    We provide an overview of the soliton perturbation theory for the N x N eigenvalue operator. Key to perturbation studies of integrable systems are the squared eigenfunctions and their adjoints, which serve as mappings between variations in the potentials and variations in the scattering data. We also address the problem of the normalization of the Jost functions, how this affects the structure and solvability of the inverse scattering equations and the definition of the scattering data. We also discuss the inner products and closure relations for these squared eigenfunctions and their adjoints.

    Journal Title

    Journal of Physics a-Mathematical and Theoretical

    Volume

    43

    Issue/Number

    43

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    18

    WOS Identifier

    WOS:000283300100020

    ISSN

    1751-8113

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