Spatial Dynamics Methods for Solitary Gravity-Capillary Water Waves with an Arbitrary Distribution of Vorticity
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/740733
- author
- Groves, Mark D. and Wahlén, Erik LU
- organization
- publishing date
- 2007
- 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
- Society for Industrial and Applied Mathematics
- 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
- 2016-04-01 11:40:05
- date last changed
- 2022-02-18 03:07:21
@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}},
keywords = {{capillarity; water waves; vorticity; bifurcation theory}},
language = {{eng}},
number = {{3}},
pages = {{932--964}},
publisher = {{Society for Industrial and Applied Mathematics}},
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}},
doi = {{10.1137/060676040}},
volume = {{39}},
year = {{2007}},
}