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Zbl 1031.76008
Fan, Enguiu; Hon, Y.C.
A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves. (English)
[J] Chaos Solitons Fractals 15, No.3, 559-566 (2003). ISSN 0960-0779

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 2000:: *76B15 Wave motions (fluid mechanics)
35Q35 Other equations arising in fluid mechanics
76B25 Solitary waves, etc. (inviscid fluids)
35Q51 Solitons

Keywords: algebraic method; travelling wave solutions; soliton; rational solutions; triangular periodic solutions; Weierstrass doubly periodic wave solutions; Jacobi elliptic periodic wave solutions

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