Title

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

Authors

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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