A unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations

A unified basic frame of rational expansion methods is presented, which leads to closed-form solutions of nonlinear evolution equations (NLEEs). The new unified algorithms are given to find exact rational formal polynomial solutions of NLEEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some physical significance NLEEs to illustrate the methods. As a consequence, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and tanh methods, but also find other new and more general solutions at the same time.