On certain new exact solutions of a diffusive predator-prey system - Kraenkel, Roberto André [UNESP]; Manikandan, K.; Senthilvelan, M. (Elsevier, 2013)
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. © 2012 Elsevier B.V.
Keywords: G'/G-Expansion method; Predator-prey system; Reaction-diffusion equations; Diffusive predator-prey system; Exact solution; Expansion methods; Nonlinear partial differential equations; Per capita; Predator - Prey system; Reaction diffusion equations; Spatio-temporal dynamics; Wave speed; Wave velocity; Ecosystems; Mathematical models; Partial differential equations; Predator prey systems; Linear equations