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Symbolic computation of exact solutions for a nonlinear evolution equation. (English) Zbl 1139.35088
Summary: By means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions are degenerated to loop-shaped solitary wave solutions for the same values of parameters producing cusp-shaped solutions and hump-shaped solutions. All these solutions are new and reported for the first time here.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35-04Machine computation, programs (partial differential equations)
35B10Periodic solutions of PDE