A New Generalized Riccati Equation Rational Expansion Method to GeneralizedBurgers–Fisher Equation with Nonlinear Terms of Any Order

Abstract

In this paper, based on a new more generalansätz, a new algebraic method, named generalized Riccatiequation rational expansion method, is devised forconstructing travelling wave solutions for nonlinear evolutionequations with nonlinear terms of any order. Compared with mostexisting tanh methods for finding travelling wave solutions, theproposed method not only recovers the results by most known algebraicmethods, but also provides new and more general solutions. We choosethe generalized Burgers–Fisher equation with nonlinear terms of anyorder to illustrate our method. As a result, we obtain several newkinds of exact solutions for the equation. This approach can also beapplied to other nonlinear evolution equations with nonlinear termsof any order.