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New solitons and periodic solutions for nonlinear physical models in mathematical physics. (English) Zbl 1196.35178

Summary: We establish exact solutions for three nonlinear equations. The sine-cosine and the exp-function methods are used to construct periodic and soliton solutions of nonlinear physical models. Many new families of exact traveling wave solutions of the nonlinear wave equations are successfully obtained. These solutions may be of significance for the explanation of some practical physical problems. It is shown that the sine-cosine and the exp-function methods provide a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
35C07 Traveling wave solutions
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