Symmetries and Integrability Properties of Generalized Fisher Type Nonlinear Diffusion Equation

TL;DR

This paper investigates the symmetry and integrability of a generalized Fisher equation, revealing various wave and static patterns through Lie symmetry analysis, contributing to understanding complex reaction-diffusion systems.

Contribution

It applies Lie symmetry analysis to a generalized Fisher equation to identify new solutions and pattern formations, advancing the study of nonlinear reaction-diffusion systems.

Findings

Discovery of traveling wave solutions

Identification of static and localized structures

Dependence of patterns on parameter choices

Abstract

Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized Fisher type equation to obtain physically interesting solutions using Lie symmetry analysis. In particular, we report several travelling wave patterns, static patterns and localized structures depending upon the choice of the parameters involved.