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Traveling waves for the Whitham equation

Ehrnström, Mats LU and Kalisch, Henrik (2009) In Differential and Integral Equations 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.
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organization
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Contribution to journal
publication status
submitted
subject
in
Differential and Integral Equations
pages
1193 - 1210
publisher
Khayyam Publishing, Inc.
ISSN
0893-4983
language
English
LU publication?
yes
id
1f611663-3996-40f8-bf7f-8a8812b5fafe (old id 1215408)
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http://www.scopus.com/record/display.url?eid=2-s2.0-84866318229&origin=inward&txGid=74D6BBAB40EF6FCBB49056BB6FED86BE.aqHV0EoE4xlIF3hgVWgA%3A1
date added to LUP
2008-10-06 16:31:31
date last changed
2016-04-16 06:12:59
@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},
  pages        = {1193--1210},
  publisher    = {Khayyam Publishing, Inc.},
  series       = {Differential and Integral Equations},
  title        = {Traveling waves for the Whitham equation},
  year         = {2009},
}