Title

Painlevé Test, Integrability, And Exact Solutions For Density-Dependent Reaction-Diffusion Equations With Polynomial Reaction Functions

Keywords

Exact solutions; Painlevé singularity analysis; Reaction-diffusion equation

Abstract

A Painlevé 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-Bäcklund 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. © 2012 Elsevier Inc. All rights reserved.

Publication Date

11-25-2012

Publication Title

Applied Mathematics and Computation

Volume

219

Issue

6

Number of Pages

3055-3064

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.amc.2012.09.032

Socpus ID

84868512591 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84868512591

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