Non-classical symmetries and the singular manifold method revisited

    Authors

    U. Tanriver;S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    J. Phys. A-Math. Gen.

    Keywords

    PARTIAL-DIFFERENTIAL EQUATIONS; INVARIANT PAINLEVE ANALYSIS; FITZHUGH-NAGUMO EQUATION; CAHN-HILLIARD EQUATIONS; SIMILARITY; REDUCTIONS; NONCLASSICAL SYMMETRIES; EVOLUTION-EQUATIONS; LONG-WAVE; LAX; PAIRS; EXPANSIONS; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    The connection between the singular manifold method (Painleve expansions truncated at the constant term) and symmetry reductions of two members of a family of Cahn-Hilliard equations is considered. The conjecture that similarity information for a nonlinear partial differential equation may always be fully recovered from the singular manifold method is violated for these equations, and is thus shown to be invalid in general. Given that several earlier examples demonstrate the connection between the two techniques in some cases, it now becomes necessary to establish when such a relationship exists-a question related to a deeper understanding of Painleve analysis. This issue is also briefly discussed.

    Journal Title

    Journal of Physics a-Mathematical and General

    Volume

    31

    Issue/Number

    5

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    1487

    Last Page

    1494

    WOS Identifier

    WOS:000071991200016

    ISSN

    0305-4470

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