Lie symmetries and travelling wave solutions of the nonlinear waves in the inhomogeneous Fisher-Kolmogorov equation

TL;DR

This paper applies Lie symmetry methods to an inhomogeneous Fisher-Kolmogorov equation with exponential spatial dependence, deriving new solutions through symmetry reductions to ordinary differential equations.

Contribution

It introduces a symmetry-based reduction approach to a specific inhomogeneous Fisher-Kolmogorov equation, leading to novel solutions not previously reported.

Findings

Derived new explicit solutions for the inhomogeneous Fisher-Kolmogorov equation.

Reduced the PDE to ODEs using symmetry methods, facilitating solution finding.

Provided interpretations of the new solutions in the context of wave propagation.

Abstract

In this work we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through two-dimensional abelian subalgebras, the equation is reduced to ordinary differential equations. New solutions have been derived and interpreted.