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Zbl 1227.76016
Constantin, Adrian; Ivanov, Rossen I.
On an integrable two-component Camassa-Holm shallow water system. (English)
[J] Phys. Lett., A 372, No. 48, 7129-7132 (2008). ISSN 0375-9601

Summary: The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this Letter we deal with such a two-component integrable system of coupled equations. First we derive the system in the context of shallow water theory. Then we show that while small initial data develop into global solutions, for some initial data wave breaking occurs. We also discuss the solitary wave solutions. Finally, we present an explicit construction for the peakon solutions in the short wave limit of system.

MSC 2000:: *76D33 Waves in incompressible viscous fluids
76B15 Wave motions (fluid mechanics)
35Q30 Stokes and Navier-Stokes equations
37J35 Completely integrable systems, etc.
35C08

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