The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations

Abstract

In recent years two nonlinear dispersive partial differential equations have attracted a lot of 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 accomodate wave breaking phenomena.

References in corpus (1)

• Inverse Scattering Transform for the Camassa-Holm equation

Cited by in corpus (5)

• On an integrable two-component Camassa-Holm shallow water system
• Long-Time Asymptotics for the Camassa-Holm Equation
• On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
• Generalised Fourier Transform and Perturbations to Soliton Equations
• Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation