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Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity

Groves, M. D. and Wahlén, Erik LU (2008) In Physica D: Nonlinear Phenomena 237(10-12). p.1530-1538
Abstract
This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of... (More)
This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
bifurcation theory, water waves, vorticity
in
Physica D: Nonlinear Phenomena
volume
237
issue
10-12
pages
1530 - 1538
publisher
Elsevier
external identifiers
  • wos:000257529200017
  • scopus:44649184941
ISSN
0167-2789
DOI
10.1016/j.physd.2008.03.015
language
English
LU publication?
yes
id
096193ec-1f5c-4921-be9a-6bea63e58788 (old id 1254596)
date added to LUP
2008-11-03 13:48:49
date last changed
2017-08-06 04:04:52
@article{096193ec-1f5c-4921-be9a-6bea63e58788,
  abstract     = {This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha &lt; alpha* and a family of periodic orbits for alpha &gt; alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved.},
  author       = {Groves, M. D. and Wahlén, Erik},
  issn         = {0167-2789},
  keyword      = {bifurcation theory,water waves,vorticity},
  language     = {eng},
  number       = {10-12},
  pages        = {1530--1538},
  publisher    = {Elsevier},
  series       = {Physica D: Nonlinear Phenomena},
  title        = {Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity},
  url          = {http://dx.doi.org/10.1016/j.physd.2008.03.015},
  volume       = {237},
  year         = {2008},
}