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Zbl 1112.76010
Shang, Yadong
Bäcklund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation. (English)
[J] Appl. Math. Comput. 187, No. 2, 1286-1297 (2007). ISSN 0096-3003

Summary: We consider the Hirota-Satsuma equation for shallow water waves. We first obtain the Bäcklund transformation and Lax pairs by using the extended homogeneous balance method. Then we find some explicit exact solutions by means of Bäcklund transformation and the extended hyperbolic function method. These solutions include the solitary wave solution of rational function type, soliton solutions, double-soliton solutions, $N$-soliton solutions, the multiple solitary wave solutions, singular solutions, and periodic wave solutions of triangle function type.

MSC 2000:: *76B15 Wave motions (fluid mechanics)
76M60 Symmetry analysis, Lie group and algebra methods
76B25 Solitary waves, etc. (inviscid fluids)
35Q51 Solitons

Keywords: Hirota-Satsuma equation; extended homogeneous balance method; extended hyperbolic function method; solitary wave

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