Abstract and Applied Analysis

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

Mehdi Nadjafikhah and Abolhassan Mahdavi

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 395847, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449898

Digital Object Identifier
doi:10.1155/2013/395847

Mathematical Reviews number (MathSciNet)
MR3139463

Zentralblatt MATH identifier
1295.35024

Citation

Nadjafikhah, Mehdi; Mahdavi, Abolhassan. Approximate Symmetry Analysis of a Class of Perturbed Nonlinear Reaction-Diffusion Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 395847, 7 pages. doi:10.1155/2013/395847. https://projecteuclid.org/euclid.aaa/1393449898


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