A new generalized Riccati equation rational expansion method to a class of nonlinear evolution equations with nonlinear terms of any order

With the aid of symbolic computation, a new algebraic method, named generalize Riccati equation rational expansion (GRERE) method, is devised for constructing travelling-wave solutions for nonlinear evolution equations (NEEs) with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling-wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. For illustration, we apply the generalized method to a class of nonlinear evolution equations with nonlinear term of any order. As a result, we obtain several new kinds of exact solutions. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.