Group classification via mapping between classes: an example of semilinear reaction-diffusion equations with exponential nonlinearity

TL;DR

This paper performs a group classification of a specific class of reaction-diffusion equations with exponential nonlinearities using a novel mapping technique between classes, advancing the understanding of their symmetry properties.

Contribution

It introduces and applies a new mapping method for classifying symmetries of reaction-diffusion equations with exponential nonlinearities.

Findings

Successful classification of symmetries for the given class of equations.

Identification of new symmetry structures through the mapping technique.

Enhanced understanding of the equations' invariance properties.

Abstract

The group classification of a class of semilinear reaction-diffusion equations with exponential nonlinearity is carried out using the technique of mapping between classes, which was recently proposed in [O.O. Vaneeva, R.O. Popovych and C. Sophocleous, Acta Appl. Math., doi:10.1007/s10440-008-9280-9, arXiv:0708.3457].