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

We construct exact solutions for a system of two coupled 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 G′G 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.

► We discuss the spatio-temporal dynamics of a predator–prey system.
► We extend G′G-expansion method to coupled partial differential equations.
► We report some exact solutions of this system.