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Fully Localised Three-Dimensional Gravity-Capillary Solitary Waves on Water of Infinite Depth

Buffoni, B. ; Groves, M. D. and Wahlén, E. LU (2022) In Journal of Mathematical Fluid Mechanics 24(2).
Abstract

Fully localised three-dimensional solitary waves are steady water waves which are evanescent in every horizontal direction. Existence theories for fully localised three-dimensional solitary waves on water of finite depth have recently been published, and in this paper we establish their existence on deep water. The governing equations are reduced to a perturbation of the two-dimensional nonlinear Schrödinger equation, which admits a family of localised solutions. Two of these solutions are symmetric in both horizontal directions and an application of a suitable variant of the implicit-function theorem shows that they persist under perturbations.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Fluid Mechanics
volume
24
issue
2
article number
55
publisher
Birkhäuser Verlag
external identifiers
  • scopus:85128713429
ISSN
1422-6928
DOI
10.1007/s00021-022-00684-5
language
English
LU publication?
yes
id
7dd1c408-02c5-439c-8a45-e20743e5e721
date added to LUP
2022-06-29 14:18:50
date last changed
2022-06-29 14:18:50
@article{7dd1c408-02c5-439c-8a45-e20743e5e721,
  abstract     = {{<p>Fully localised three-dimensional solitary waves are steady water waves which are evanescent in every horizontal direction. Existence theories for fully localised three-dimensional solitary waves on water of finite depth have recently been published, and in this paper we establish their existence on deep water. The governing equations are reduced to a perturbation of the two-dimensional nonlinear Schrödinger equation, which admits a family of localised solutions. Two of these solutions are symmetric in both horizontal directions and an application of a suitable variant of the implicit-function theorem shows that they persist under perturbations.</p>}},
  author       = {{Buffoni, B. and Groves, M. D. and Wahlén, E.}},
  issn         = {{1422-6928}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{Birkhäuser Verlag}},
  series       = {{Journal of Mathematical Fluid Mechanics}},
  title        = {{Fully Localised Three-Dimensional Gravity-Capillary Solitary Waves on Water of Infinite Depth}},
  url          = {{http://dx.doi.org/10.1007/s00021-022-00684-5}},
  doi          = {{10.1007/s00021-022-00684-5}},
  volume       = {{24}},
  year         = {{2022}},
}