The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations

Abstract

In recent years two nonlinear dispersive partial differential equations have attracted a lot of attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin-Bona-Mahoney and Korteweg-de Vries equations. In particular, they accomodate wave breaking phenomena.

References in corpus (1)

• Inverse Scattering Transform for the Camassa-Holm equation

Cited by in corpus (72)

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• Hamiltonian structure for two-dimensional extended Green-Naghdi equations
• Variational derivation of two-component Camassa-Holm shallow water system
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• Well-posedness of a highly nonlinear shallow water equation on the circle
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• On the Cauchy problem for a two-component Degasperis-Procesi system
• Non-uniform dependence for the two-component Camassa-Holm shallow water system
• The algebro-geometric solutions for Degasperis-Procesi hierarchy
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• Non-uniform dependence for higher dimensional Camassa-Holm equations in Besov spaces
• Non-uniform dependence for the Novikov equation in Besov spaces
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• Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space
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