Group classification of variable coefficient quasilinear reaction-diffusion equations

TL;DR

This paper performs an exhaustive group classification of variable coefficient quasilinear reaction-diffusion equations, leveraging a conditional equivalence group to identify symmetries and transformations.

Contribution

It introduces a novel approach using a conditional equivalence group to classify symmetries of reaction-diffusion equations with variable coefficients.

Findings

Complete classification of symmetries for the given class of equations.

Identification of admissible point transformations within the class.

Development of a framework for analyzing variable coefficient reaction-diffusion equations.

Abstract

The group classification of variable coefficient quasilinear reaction-diffusion equations $u_t=u_{xx}+h(x)B(u)$ is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformation within the class.