Lie symmetries of a generalized Fisher equation in cylindrical coordinates

TL;DR

This paper analyzes a generalized Fisher equation in cylindrical coordinates using Lie symmetry methods, identifying conditions for additional symmetries and deriving reduced ODEs.

Contribution

It determines specific source functions that admit non-trivial Lie symmetries beyond time translation, and derives corresponding reduced equations.

Findings

Identifies source functions leading to extra Lie symmetries.

Derives reduced ordinary differential equations from symmetries.

Provides conditions for exponential diffusion functions.

Abstract

In this work we studied a generalized Fisher equation in cylindrical coordinate using Lie symmetry method. We have determined for what type of source function the generalized Fisher equation has Lie Symmetries other than time translation symmetry when the diffusion function is given by an exponential function. Also the reduced ordinary differential equations are obtained corresponding to Lie symmetries of the generalized Fisher equation.