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Abstract and Applied Analysis
Volume 2013, Article ID 395847, 7 pages
http://dx.doi.org/10.1155/2013/395847
Research Article

Approximate Symmetry Analysis of a Class of Perturbed Nonlinear Reaction-Diffusion Equations

Department of Mathematics, Islamic Azad University, Karaj Branch, P.O. Box 31485-313, Karaj, Iran

Received 4 July 2013; Accepted 11 November 2013

Academic Editor: Maria Bruzón

Copyright © 2013 Mehdi Nadjafikhah and Abolhassan Mahdavi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of approximate symmetries of a class of nonlinear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we have applied the method which was proposed by Fushchich and Shtelen (1989) and fundamentally based on the expansion of the dependent variables in a perturbation series. Particularly, an optimal system of one-dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.