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
Copyright Status
Unknown
Socpus ID
84868512591 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84868512591
STARS Citation
Hearns, Jessica; Van Gorder, Robert A.; and Roy Choudhury, S., "Painlevé Test, Integrability, And Exact Solutions For Density-Dependent Reaction-Diffusion Equations With Polynomial Reaction Functions" (2012). Scopus Export 2010-2014. 4781.
https://stars.library.ucf.edu/scopus2010/4781