, Volume 192, Issue 1, pp 165-186
Date: 30 May 2008

The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

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Abstract

In recent years two nonlinear dispersive partial differential equations have attracted much 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 accommodate wave breaking phenomena.

Communicated by L. Ambrosio