  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.
