A generalization of (G′/G)-expansion method and its application to nonlinear reaction-diffusion equations arising in mathematical biology

In this paper, by introducing a proper transformation, the (G'/G)-expansion method is further extended into the nonlinear reaction-diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.