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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:
35Q53KdV-like (Korteweg-de Vries) equations
35B10Periodic solutions of PDE
35C08Soliton solutions of PDE
35C07Traveling wave solutions of PDE