Travelling wave solutions for combined and double combined sine–cosine-Gordon equations by the variable separated ODE method

A combined sine–cosine-Gordon and a double combined sine–cosine-Gordon equations, that combine the effects of sine and cosine, are investigated. The analysis rests mainly on the newly developed variable separated ODE method [Sirendaoreji, Sun Jiong, A direct method for solving sinh-Gordon type equation, Phys. Lett. A 298 (2002) 133–139]. Exact travelling wave solutions for the combined equations are formally derived by using this method. The work emphasizes the power of the method that can be used in problems of identical nonlinearities.