On certain new exact solutions of a diffusive predator-prey system

TL;DR

This paper derives exact solutions for a predator-prey model with Allee effect using the rac{G'}{G}xpansion method, revealing different wave solutions and their biological implications.

Contribution

It introduces exact solutions for a predator-prey system with Allee effect using a novel analytical method for multiple wave speeds.

Findings

Multiple exact wave solutions identified for different velocities.

Solutions demonstrate the impact of Allee effect on predator-prey dynamics.

Biological relevance of solutions discussed.

Abstract

We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the $\big(\frac{G'}{G}\big)$ expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained.