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

TL;DR

This paper analyzes approximate symmetries of perturbed nonlinear reaction-diffusion equations, specifically the KPP equation, using perturbation series and constructs invariant solutions.

Contribution

It applies a perturbation-based method to find approximate symmetries and invariant solutions for the KPP equation, advancing symmetry analysis in nonlinear PDEs.

Findings

Constructed an optimal system of one-dimensional subalgebras.

Derived invariant solutions corresponding to the symmetries.

Extended symmetry analysis to perturbed reaction-diffusion equations.

Abstract

In this paper, the problem of approximate symmetries of a class of non-linear 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 [8] 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.