Fully Localised Three-Dimensional Gravity-Capillary Solitary Waves on Water of Infinite Depth
(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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https://lup.lub.lu.se/record/7dd1c408-02c5-439c-8a45-e20743e5e721
- author
- Buffoni, B. ; Groves, M. D. and Wahlén, E. LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Fluid Mechanics
- volume
- 24
- issue
- 2
- article number
- 55
- publisher
- Birkhäuser
- 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
- 2024-09-05 19:24:46
@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}}, 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}}, }