A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension
(2018) In Archive for Rational Mechanics and Analysis 228(3). p.773-820- Abstract
Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity–capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as ‘lumps’), and a mathematically rigorous existence theory for strong surface tension (Bond number (Formula presented.) greater than (Formula presented.)) has recently been given. In this article we present an existence theory for the physically more realistic case (Formula presented.). A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle... (More)
Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity–capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as ‘lumps’), and a mathematically rigorous existence theory for strong surface tension (Bond number (Formula presented.) greater than (Formula presented.)) has recently been given. In this article we present an existence theory for the physically more realistic case (Formula presented.). A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey–Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.
(Less)
- author
- Buffoni, Boris ; Groves, Mark D. and Wahlén, Erik LU
- organization
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Archive for Rational Mechanics and Analysis
- volume
- 228
- issue
- 3
- pages
- 773 - 820
- publisher
- Springer
- external identifiers
-
- scopus:85037642362
- ISSN
- 0003-9527
- DOI
- 10.1007/s00205-017-1205-1
- project
- Nonlinear Water Waves
- language
- English
- LU publication?
- yes
- id
- 725bcd15-3578-4011-98e3-46584495c40b
- date added to LUP
- 2017-12-21 10:05:54
- date last changed
- 2022-03-09 08:06:41
@article{725bcd15-3578-4011-98e3-46584495c40b,
abstract = {{<p>Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity–capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as ‘lumps’), and a mathematically rigorous existence theory for strong surface tension (Bond number (Formula presented.) greater than (Formula presented.)) has recently been given. In this article we present an existence theory for the physically more realistic case (Formula presented.). A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey–Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.</p>}},
author = {{Buffoni, Boris and Groves, Mark D. and Wahlén, Erik}},
issn = {{0003-9527}},
language = {{eng}},
number = {{3}},
pages = {{773--820}},
publisher = {{Springer}},
series = {{Archive for Rational Mechanics and Analysis}},
title = {{A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension}},
url = {{http://dx.doi.org/10.1007/s00205-017-1205-1}},
doi = {{10.1007/s00205-017-1205-1}},
volume = {{228}},
year = {{2018}},
}