Separation of variables in PDEs using nonlinear transformations: Applications to reaction–diffusion type equations

Abstract

The paper describes a new approach to constructing exact solutions of nonlinear partial differential equations that employs separation of variables using special (nonlinear integral) transformations and the splitting principle. To illustrate its effectiveness, the method is applied to nonlinear reaction–diffusion type equations that involve variable coefficients and arbitrary functions. New exact functional separable solutions as well as generalized traveling wave solutions are obtained.