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Spatial Dynamics Methods for Solitary Gravity-Capillary Water Waves with an Arbitrary Distribution of Vorticity

Groves, Mark D. and Wahlén, Erik LU (2007) In SIAM Journal on Mathematical Analysis 39(3). p.932-964
Abstract
This paper presents existence theories for several families of small-amplitude solitary-wave solutions to the classical two-dimensional water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the timelike variable. A center-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom. Homoclinic solutions to the... (More)
This paper presents existence theories for several families of small-amplitude solitary-wave solutions to the classical two-dimensional water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the timelike variable. A center-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom. Homoclinic solutions to the reduced system, which correspond to solitary water waves, are detected by a variety of dynamical systems methods. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
capillarity, water waves, vorticity, bifurcation theory
in
SIAM Journal on Mathematical Analysis
volume
39
issue
3
pages
932 - 964
publisher
SIAM
external identifiers
  • wos:000251174300010
  • scopus:44649159515
ISSN
0036-1410
DOI
10.1137/060676040
language
English
LU publication?
yes
id
0478dcae-1a28-417c-9df1-874a60405528 (old id 740733)
date added to LUP
2008-01-09 14:15:46
date last changed
2017-04-30 06:49:13
@article{0478dcae-1a28-417c-9df1-874a60405528,
  abstract     = {This paper presents existence theories for several families of small-amplitude solitary-wave solutions to the classical two-dimensional water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the timelike variable. A center-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom. Homoclinic solutions to the reduced system, which correspond to solitary water waves, are detected by a variety of dynamical systems methods.},
  author       = {Groves, Mark D. and Wahlén, Erik},
  issn         = {0036-1410},
  keyword      = {capillarity,water waves,vorticity,bifurcation theory},
  language     = {eng},
  number       = {3},
  pages        = {932--964},
  publisher    = {SIAM},
  series       = {SIAM Journal on Mathematical Analysis},
  title        = {Spatial Dynamics Methods for Solitary Gravity-Capillary Water Waves with an Arbitrary Distribution of Vorticity},
  url          = {http://dx.doi.org/10.1137/060676040},
  volume       = {39},
  year         = {2007},
}