On the Existence and Conditional Energetic Stability of Solitary Gravity-Capillary Surface Waves on Deep Water
(2011) In Journal of Mathematical Fluid Mechanics 13(4). p.593-627- Abstract
- This paper presents an existence and stability theory for gravity-capillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set D-mu of minimisers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic... (More)
- This paper presents an existence and stability theory for gravity-capillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set D-mu of minimisers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic focussing nonlinearity. We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model equation as mu down arrow 0. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2377716
- author
- Groves, M. D. and Wahlén, Erik LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Fluid Mechanics
- volume
- 13
- issue
- 4
- pages
- 593 - 627
- publisher
- Birkhäuser Verlag
- external identifiers
-
- wos:000300352500007
- scopus:80855165477
- ISSN
- 1422-6928
- DOI
- 10.1007/s00021-010-0034-x
- language
- English
- LU publication?
- yes
- id
- 1849dc9d-8056-40d1-b433-e7f3de6d851c (old id 2377716)
- date added to LUP
- 2016-04-01 12:59:07
- date last changed
- 2022-03-06 03:06:24
@article{1849dc9d-8056-40d1-b433-e7f3de6d851c,
abstract = {{This paper presents an existence and stability theory for gravity-capillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set D-mu of minimisers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic focussing nonlinearity. We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model equation as mu down arrow 0.}},
author = {{Groves, M. D. and Wahlén, Erik}},
issn = {{1422-6928}},
language = {{eng}},
number = {{4}},
pages = {{593--627}},
publisher = {{Birkhäuser Verlag}},
series = {{Journal of Mathematical Fluid Mechanics}},
title = {{On the Existence and Conditional Energetic Stability of Solitary Gravity-Capillary Surface Waves on Deep Water}},
url = {{http://dx.doi.org/10.1007/s00021-010-0034-x}},
doi = {{10.1007/s00021-010-0034-x}},
volume = {{13}},
year = {{2011}},
}