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New exact periodic solutions to a category of nonlinear evolution equations. (Chinese. English summary) Zbl 1087.35506

Summary: Based on the original expansion method of Jacobi elliptic functions, other Jacobi elliptic functions are introduced and the expansion method of Jacobi elliptic functions presented by Liu is expanded. Taking the modified Benjamin-Bona-Malong equation and the Gardner equation as examples, a series of new exact periodic solutions are obtained for these equations which are found with the help of mathematics software Mathematica. These solutions can degenerate into solitary wave solutions or trigonometric function solutions under a critical condition.

MSC:

35B10 Periodic solutions to PDEs
35K55 Nonlinear parabolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C10 Series solutions to PDEs

Software:

Mathematica
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