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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.

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Authors and Affiliations

  1. School of Mathematics, Trinity College, Dublin 2, Ireland

    Adrian Constantin

  2. Université Bordeaux I, IMB and CNRS UMR 5251, 351 Cours de la Libération, 33405, Talence Cedex, France

    David Lannes

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  1. Adrian Constantin
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  2. David Lannes
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Correspondence to Adrian Constantin.

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Communicated by L. Ambrosio

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Constantin, A., Lannes, D. The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations. Arch Rational Mech Anal 192, 165–186 (2009). https://doi.org/10.1007/s00205-008-0128-2

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  • DOI: https://doi.org/10.1007/s00205-008-0128-2

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