Article

Archive for Rational Mechanics and Analysis

, Volume 192, Issue 1, pp 165-186

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

  • Adrian ConstantinAffiliated withSchool of Mathematics, Trinity College Email author 
  • , David LannesAffiliated withUniversité Bordeaux I, IMB and CNRS UMR 5251

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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.