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A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves. (English) Zbl 1031.76008
Summary: A new algebraic method is devised to uniformly construct a series of new travelling wave solutions for two variant Boussinesq equations. The solutions obtained in this paper include soliton solutions, rational solutions, triangular periodic solutions, and Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions under a certain limit condition. Compared with existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify various types of solutions according to some parameters.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35PDEs in connection with fluid mechanics
76B25Solitary waves (inviscid fluids)
35Q51Soliton-like equations
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