Painleve Analysis And Special Solutions For A Class Of Cahn-Hilliard Equations

    Authors

    S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Can. J. Phys.

    Keywords

    PARTIAL-DIFFERENTIAL EQUATIONS; LINEAR EVOLUTION-EQUATIONS; BACKLUND; TRANSFORMATION; P-TYPE; PROPERTY; CONNECTION; INVARIANT; Physics, Multidisciplinary

    Abstract

    A Painleve analysis of a family of Cahn-Hilliard equations (with diffusion coefficients of the form D(U) = SIGMA-m(i=0) (D(i)U(i)) is performed. For m = 2, the equation fails the Painleve test. Of the other cases of physical interest, the case m = 1 has only the conditional Painleve property; while the cases m = 3, 4 are weak Painleve, suggesting that the equation is partially integrable for these cases. For the cases m = 1 and m = 2, an auto-Backlund transformation between two solutions is constructed, leading to classes of analytical solutions of the equations. Special analytical solutions for all m greater-than-or-equal-to 3 are also constructed.

    Journal Title

    Canadian Journal of Physics

    Volume

    70

    Issue/Number

    4

    Publication Date

    1-1-1992

    Document Type

    Article

    Language

    English

    First Page

    273

    Last Page

    281

    WOS Identifier

    WOS:A1992JC71000012

    ISSN

    0008-4204

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