On an integrable two-component Camassa–Holm shallow water system

By Adrian Constantin, Rossen I. Ivanov. 2008

473 citations recorded by the source corpus.

Abstract 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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76296f81044dbebd5adb763282d2913d3d9e53be

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Citations in the corpus

Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “[7, 18 ,25] andreferencestherein.System(1.4)isintegrable.However,itdoesnothavethepeakon solitons in the form of a superposition of multi-peakons.”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, background): “[14] A. Constantin, R. Ivanov, On an integrable two-component Camassa-Holm shallow water system, Phys.”
Global weak solutions for a two-component Camassa–Holm shallow water system (2011, methodology): “[37] R.I. Ivanov, Water waves and integrability, Philos.”
THE GEOMETRY OF THE TWO-COMPONENT CAMASSA-HOLM AND DEGASPERIS-PROCESI EQUATIONS (2010, background): “A derivation of (2CH) in the context of shallow water waves appears in [4].”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, methodology): “Now we want to construct a Lyapunov function for our system, as in [20].”
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, methodology): “[23] R. Ivanov, Two-component integrable systems modelling shallow water waves: The constant vorticity case, Wave Motion 46 (2009) 389–396.”
On the Cauchy problem for the two-component Camassa–Holm system (2011, methodology): “Recently, Constantin and Ivanov [13] gave a rigorous justification of the derivation of System (1.”