Exact solutions to a large class of nonlinear evolution equations

A unified approach is presented for finding the travelling wave solutions to a large class of nonlinear evolution equations defined by the concept of "rank". The key idea of this method is to make use of the arbitrariness of the Painlevé analysis manifold. We selected a new expansion variable, thus obtaining a rich variety of exact travelling wave solutions to a nonlinear evolution equation, including solitary wave solutions, triangular periodic solutions and Jacobi periodic wave solutions, as well as rational solutions and so on. This method is completely algorithmic, hence the Maple implementation is also used. Several examples illustrate the capabilities of the package; new solutions and more general types of solutions are obtained for some nonlinear evolution equations.