Archive for Rational Mechanics and Analysis

, 192:165

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

Authors

    • School of MathematicsTrinity College
  • David Lannes
    • Université Bordeaux I, IMB and CNRS UMR 5251
Article

DOI: 10.1007/s00205-008-0128-2

Cite this article as:
Constantin, A. & Lannes, D. Arch Rational Mech Anal (2009) 192: 165. doi:10.1007/s00205-008-0128-2

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.

Copyright information

© Springer-Verlag 2008