Painleve test, integrability, and exact solutions for density-dependent reaction-diffusion equations with polynomial reaction functions

    Authors

    J. Hearns; R. A. Van Gorder;S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Reaction-diffusion equation; Painleve singularity analysis; Exact; solutions; PARTIAL-DIFFERENTIAL EQUATIONS; FITZHUGH-NAGUMO EQUATION; HOMOTOPY; ANALYSIS METHOD; BACKLUND TRANSFORMATION; KURAMOTO-SIVASHINSKY; SYMBOLIC; COMPUTATION; WAVE SOLUTIONS; PROPERTY; SYSTEM; Mathematics, Applied

    Abstract

    A Painleve test is performed for a general density-dependent reaction-diffusion equation, where the reaction function takes the form of an Nth order polynomial, in order to determine the member models of this class which are integrable. First, we determine the equilibrium behavior for the model. Then, truncated Laurent expansions, relevant to equations having movable branch points at leading order, are used to construct special solutions for the three integrable classes of reaction-diffusion equations which were found. An auto-Backlund transformation between two solutions is constructed for an equation having a pole at leading order, which can be used to find further solutions. Some of the solutions are new, and through certain simplifications we may recover old solutions as well. (C) 2012 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    219

    Issue/Number

    6

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    3055

    Last Page

    3064

    WOS Identifier

    WOS:000310649900021

    ISSN

    0096-3003

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