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

TL;DR

This paper demonstrates that the Camassa-Holm and Degasperis-Procesi equations are relevant for modeling shallow water wave propagation, capturing nonlinear effects and wave breaking phenomena beyond classical models.

Contribution

It establishes the hydrodynamical relevance of these two integrable equations in shallow water wave modeling, highlighting their ability to describe wave breaking.

Findings

Both equations model shallow water wave propagation.

They incorporate stronger nonlinear effects than classical models.

They can describe wave breaking phenomena.

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.