Exact solutions to the double Sine-Gordon equation

The double Sine-Gordon equation (DSG) with arbitrary constant coefficients is studied by F-expansion method, which can be thought of as an over-all generalization of the Jacobi elliptic function expansion since F here stands for every one of the Jacobi elliptic functions (even other functions). We first derive three kinds of the generic solutions of the DSG as well as the generic solutions of the Sine-Gordon equation (SG), then in terms of Appendix A, many exact periodic wave solutions, solitary wave solutions and trigonometric function solutions of the DSG are separated from its generic solutions. The corresponding results of the SG, which is a special case of the DSG, can also be obtained.