Archive for Rational Mechanics and Analysis

, Volume 192, Issue 1, pp 165–186 | Cite as

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

  • Adrian Constantin
  • David Lannes


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.


Water Wave Wave Breaking Holm Equation Maximal Existence Time Plunging Breaker 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of MathematicsTrinity CollegeDublin 2Ireland
  2. 2.Université Bordeaux I, IMB and CNRS UMR 5251Talence CedexFrance

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