Application of the G′/G-expansion method for nonlinear diffusion equations with nonlinear source

The generalized diffusion equations, with nonlinear source terms which encompasses the Fisher, Newell–Whitehead, FitzHugh–Nagumo and Allen–Cahn equations as particular forms are solved by the G′/G-expansion method. The exact solutions are in terms of hyperbolic, trigonometric and rational functions with external parameters. This paper concludes with the stationary topological soliton solution of the FitzHugh–Nagumo equation that is obtained by the Ansatz method.