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Zbl 1231.76040
Ivanov, Rossen
Two-component integrable systems modelling shallow water waves: the constant vorticity case. (English)
[J] Wave Motion 46, No. 6, 389-396 (2009). ISSN 0165-2125

Summary: We describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system.

MSC 2000:: *76B15 Wave motions (fluid mechanics)
35Q35 Other equations arising in fluid mechanics
37K10 Completely integrable systems etc.
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Keywords: water wave; vorticity; Camassa-Holm equation; Zakharov-Itô system; Kaup-Boussinesq system; Lax pair; soliton; peakon

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Zentralblatt MATH Berlin [Germany]