A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations

A new elliptic equation rational expansion method is presented by a new general ansätz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich new families of the exact solutions, including rational form solitary wave, rational form triangular periodic, rational form Jacobi and Weierstrass doubly periodic solutions.