Traveling wave solutions of the (N+1)-dimensional sine-cosine-Gordon equation

In this study, an isteresting method that assumes phi' = f (sin(phi)) is used for solving the (N + 1)-dimensional sine-cosine-Gordon equation. A new elliptic integral function solution is obtained by this technique, and then this solution is converted into the Jacobi elliptic function solution. This methodology can be applied to solve other types of sine-cosine-Gordon equations.