On the asymptotic solutions of the KdV equation with higher-order corrections

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    4 Scopus citations

    Abstract

    A method for construction of new integrable PDEs, whose properties are related to an asymptotic perturbation expansion with the leading-order term given by an integrable equation, is developed. A new integrable equation is constructed by applying the properly defined Lie-Bäcklund group of transformations to the leading-order equation. The integrable equations related to the Korteweg-de Vries (KdV) equation with higher-order corrections are used to investigate the limits of applicability of the so-called asymptotic integrability concept. It is found that the solutions of the higher-order KdV equations obtained by a near identity transform from the normal form solitary waves cannot, in principle, describe some intrinsic features of the high-order KdV solitons.

    Original languageEnglish
    Pages (from-to)1443-1461
    Number of pages19
    JournalNonlinearity
    Volume18
    Issue number4
    DOIs
    StatePublished - 1 Jul 2005

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • Physics and Astronomy (all)
    • Applied Mathematics

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