Traveling waves for the Whitham equation
(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:
https://lup.lub.lu.se/record/1215408
- author
- Ehrnström, Mats LU and Kalisch, Henrik
- organization
- publishing date
- 2009
- 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
- 2022-03-31 01:04:31
@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}}, }