Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

DOI

10.2991/jnmp.2006.13.3.8How to use a DOI?

Keywords

Nonlocal Dispersive Wave Equations, Wave Breaking, Korteweg de Vries (KdV) equation

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive differential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Hailiang Liu
PY  - 2006
DA  - 2006/08/01
TI  - Wave Breaking in a Class of Nonlocal Dispersive Wave Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 441
EP  - 466
VL  - 13
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.3.8
DO  - 10.2991/jnmp.2006.13.3.8
ID  - Liu2006
ER  -