The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
- First Online:
- Cite this article as:
- Constantin, A. & Lannes, D. Arch Rational Mech Anal (2009) 192: 165. doi:10.1007/s00205-008-0128-2
- 449 Views
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.