The extended Jacobi Elliptic Functions expansion method and new exact solutions for the Zakharov equations

Abstract. We extended the Jacobi elliptic function expansion method by constructing four new Jacobian elliptic functions, and apply this method to Zakharov equations for illustration, abundant new doubly periodic solutions are obtained, these solutions are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0, which shows that the new method is more powerful to seek the exact solutions of the nonlinear partial differential equations in mathematical physics.