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Traveling waves for the Whitham equation

Ehrnström, Mats LU and Kalisch, Henrik (2009) In Differential and Integral Equations 22(11-12). p.1193-1210
Abstract
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves on finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities approach the limiting long-wave speed c0, and the waves approach a solitary wave. It is also shown that there can be no solitary waves with velocities much greater than c0. Finally, numerical approximations of some periodic traveling waves are presented.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Differential and Integral Equations
volume
22
issue
11-12
pages
1193 - 1210
publisher
Khayyam Publishing, Inc.
external identifiers
  • scopus:84866318229
ISSN
0893-4983
language
English
LU publication?
yes
id
1f611663-3996-40f8-bf7f-8a8812b5fafe (old id 1215408)
date added to LUP
2016-04-04 09:06:15
date last changed
2021-08-25 03:30:17
@article{1f611663-3996-40f8-bf7f-8a8812b5fafe,
  abstract     = {The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves on finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities approach the limiting long-wave speed c0, and the waves approach a solitary wave. It is also shown that there can be no solitary waves with velocities much greater than c0. Finally, numerical approximations of some periodic traveling waves are presented.},
  author       = {Ehrnström, Mats and Kalisch, Henrik},
  issn         = {0893-4983},
  language     = {eng},
  number       = {11-12},
  pages        = {1193--1210},
  publisher    = {Khayyam Publishing, Inc.},
  series       = {Differential and Integral Equations},
  title        = {Traveling waves for the Whitham equation},
  url          = {https://lup.lub.lu.se/search/files/5232594/1215421.pdf},
  volume       = {22},
  year         = {2009},
}