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

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.