The binary F-expansion method and its application for solving the (n + 1)-dimensional sine-Gordon equation

In this paper, the binary F-expansion method with two wave speeds has been introduced based on the traditional F-expansion method. Using this new extend method and a simple transformation technique, the (n + 1)-dimensional sine-Gordon equation was studied. By appendix table of the Jacobi elliptic functions with modulus m 1 and m 2 , many double-periodic solutions were obtained. When the modulus m 1 , m 2 approach to 1 or 0, we obtained simultaneously many breather solutions of solitary wave, kink and anti-kink wave, and double kink and anti-kink wave. Many new solutions were obtained.