Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities

TL;DR

This paper classifies variable coefficient reaction-diffusion equations with exponential nonlinearities using group analysis, describing transformations, symmetries, and limits to power nonlinearities, advancing understanding of their structure and solutions.

Contribution

It provides a comprehensive group classification, describes admissible transformations, and studies limit processes between exponential and power nonlinear reaction-diffusion equations.

Findings

Complete family of maximal normalized subclasses identified

Admissible transformations exhaustively described

Limit processes between equations with different nonlinearities analyzed

Abstract

The group classification of a class of variable coefficient reaction-diffusion equations with exponential nonlinearities is carried out up to both the equivalence generated by the corresponding generalized equivalence group and the general point equivalence. The set of admissible transformations of this class is exhaustively described via finding the complete family of maximal normalized subclasses and associated conditional equivalence groups. Limit processes between variable coefficient reaction-diffusion equations with power nonlinearities and those with exponential nonlinearities are simultaneously studied with limit processes between objects related to these equations (including Lie symmetries, exact solutions and conservation laws).