A new method applied to obtain complex Jacobi elliptic function solutions of general nonlinear equations

Based on computerized symbolic computation, a new complex Jacobi elliptic function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equation be the superposition of different powers of the Jacobi elliptic function. By finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex Jacobi elliptic function. The characteristic feature of this method is that, without transformation, we can derive exact solutions to the general nonlinear equations directly. Some illustrative equations, such as the (1 + 1)-dimensional Klein–Gordon– Zakharov equation, (2 + 1)-dimensional long-wave–short-wave resonance interaction equation, are investigated by this means to find the new exact solutions.