Exact time-dependent solutions of a Fisher-KPP-like equation obtained with nonclassical symmetry analysis

TL;DR

This paper derives exact, time-dependent solutions for a nonlinear reaction-diffusion equation related to the Fisher-KPP model using nonclassical symmetry analysis, expanding the set of known solutions for applications in biology and ecology.

Contribution

It introduces a novel method to obtain exact time-dependent solutions of a Fisher-KPP-like equation through nonclassical symmetry analysis, which is rare in the literature.

Findings

Exact solutions are constructed for a reaction-diffusion model.

The solutions connect to the classical Fisher-KPP model in a specific limit.

Provides new analytical tools for studying biological invasion and related processes.

Abstract

We consider a family of exact solutions to a nonlinear reaction-diffusion model, constructed using nonclassical symmetry analysis. In a particular limit, the mathematical model approaches the well-known Fisher-KPP model, which means that it is related to various applications including cancer progression, wound healing and ecological invasion. The exact solution is mathematically interesting since exact solutions of the Fisher-KPP model are rare, and often restricted to long-time travelling wave solutions for special values of the travelling wave speed.