Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method. (English) Zbl 1099.65095

Summary: 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 ordinary differential equation method by Sirendaoreji and S. Jiong [Phys. Lett., A 298, No. 2–3, 133–139 (2002; Zbl 0995.35056)]. 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.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)


Zbl 0995.35056
Full Text: DOI


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