CLASSIFICATION OF TWO TYPES OF WEAK SOLUTIONS TO THE CASIMIR EQUATION FOR THE ITO SYSTEM

    Authors

    J. Haussermann;R. A. van Gorder

    Comments

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    Abbreviated Journal Title

    Q. Appl. Math.

    Keywords

    Casimir equation; Ito system; extended KdV equation; weak solutions; asymptotic series; Mathematics, Applied

    Abstract

    The existence and non-uniqueness of two classes of weak solutions to the Casimir equation for the Ito system is discussed. In particular, for (i) all possible travelling wave solutions and (ii) one vital class of self-similar solutions, all possible families of local power series solutions are found. We are then able to extend both types of solutions to the entire real line, obtaining separate classes of weak solutions to the Casimir equation. Such results constitute rare globally valid analytic solutions to a class of nonlinear wave equations. Closed-form asymptotic approximations are also given in each case, and these agree nicely with the numerical solutions available in the literature.

    Journal Title

    Quarterly of Applied Mathematics

    Volume

    72

    Issue/Number

    3

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    471

    Last Page

    490

    WOS Identifier

    WOS:000346651300003

    ISSN

    0033-569X

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