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Bäcklund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation. (English) Zbl 1112.76010
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.

76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
76B25Solitary waves (inviscid fluids)
35Q51Soliton-like equations
Full Text: DOI
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