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Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine-cosine method. (English) Zbl 1115.35117
Summary: We establish exact solutions for coupled nonlinear evolution equations. The sine-cosine method is used to construct exact periodic and soliton solutions of coupled nonlinear evolution equations. Many new families of exact travelling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky equations and the coupled nonlinear Klein-Gordon and Nizhnik-Novikov-Veselov equations are successfully obtained. The obtained solutions include compactons, solitons, solitary patterns and periodic solutions.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
37K40Soliton theory, asymptotic behavior of solutions
35Q51Soliton-like equations