A scaling transformation method and exact solutions of nonlinear reaction–diffusion model

Abstract

We find a very simple scaling transformation method by which a kind of rank non-homogenous second order nonlinear ODEs is reduced to an integral form. Comparing with the canonical-like transformation method and the first integral method, our method provides a simple mechanism of reduction of such equations. As an application, a reaction–diffusion equation with variable coefficients is integrated, and its exact cnoidal wave solution is obtained. Furthermore, by using the complete discrimination system for polynomial method, more exact solutions are obtained.