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

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

2007-09-06

arxiv.org/abs/0709.0905v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00205-008-0128-2

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.

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