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Solitons from the Lagrangian perspective

Constantin, Adrian LU (2007) In Discrete and Continuous Dynamical Systems. Series A 19(3). p.469-481
Abstract
The soliton solution of the Korteweg-de Vries equation provides a good approximation to the shape of a solitary wave solution to the governing equations for water waves. However, the corresponding velocity field below the soliton is not an accurate approximation. We propose an approach that provides us with a better approximation. By describing the particle paths below the free surface, we show that the qualitative features of the entire flow in a solitary water wave is captured by our approximation of the velocity field.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
particle trajectory, solitary wave, soliton
in
Discrete and Continuous Dynamical Systems. Series A
volume
19
issue
3
pages
469 - 481
publisher
American Institute of Mathematical Sciences
external identifiers
  • wos:000248775000002
  • scopus:37349047161
ISSN
1553-5231
language
English
LU publication?
yes
id
ea94fcbc-2c9d-4c0a-8717-82617253fe2a (old id 692711)
alternative location
http://www.aimsciences.org/journals/doIpChk.jsp?paperID=2709&mode=full
date added to LUP
2007-12-06 11:19:25
date last changed
2017-01-08 05:11:03
@article{ea94fcbc-2c9d-4c0a-8717-82617253fe2a,
  abstract     = {The soliton solution of the Korteweg-de Vries equation provides a good approximation to the shape of a solitary wave solution to the governing equations for water waves. However, the corresponding velocity field below the soliton is not an accurate approximation. We propose an approach that provides us with a better approximation. By describing the particle paths below the free surface, we show that the qualitative features of the entire flow in a solitary water wave is captured by our approximation of the velocity field.},
  author       = {Constantin, Adrian},
  issn         = {1553-5231},
  keyword      = {particle trajectory,solitary wave,soliton},
  language     = {eng},
  number       = {3},
  pages        = {469--481},
  publisher    = {American Institute of Mathematical Sciences},
  series       = {Discrete and Continuous Dynamical Systems. Series A},
  title        = {Solitons from the Lagrangian perspective},
  volume       = {19},
  year         = {2007},
}