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Variational existence theory for hydroelastic solitary waves : Une théorie variationnelle d'existence d'ondes solitaires hydroélastiques

Groves, Mark D. ; Hewer, Benedikt and Wahlén, Erik LU orcid (2016) In Comptes Rendus Mathématique 354(11). p.1078-1086
Abstract

This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for sufficiently large values of a dimensionless parameter γ. We establish the existence of a minimiser of the wave energy E subject to the constraint I=2μ, where I is the horizontal impulse and 0<μ≪1, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions to the nonlinear Schrödinger equation with cubic focussing nonlinearity as μ↓0.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Comptes Rendus Mathématique
volume
354
issue
11
pages
9 pages
publisher
Elsevier
external identifiers
  • wos:000388360700006
  • scopus:84994123732
ISSN
1631-073X
DOI
10.1016/j.crma.2016.10.004
project
Nonlinear Water Waves
language
English
LU publication?
yes
id
f6487d0b-dbeb-4f62-9a58-49d32f165d86
date added to LUP
2016-11-21 09:54:56
date last changed
2025-02-22 19:17:05
@article{f6487d0b-dbeb-4f62-9a58-49d32f165d86,
  abstract     = {{<p>This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for sufficiently large values of a dimensionless parameter γ. We establish the existence of a minimiser of the wave energy E subject to the constraint I=2μ, where I is the horizontal impulse and 0&lt;μ≪1, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions to the nonlinear Schrödinger equation with cubic focussing nonlinearity as μ↓0.</p>}},
  author       = {{Groves, Mark D. and Hewer, Benedikt and Wahlén, Erik}},
  issn         = {{1631-073X}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{11}},
  pages        = {{1078--1086}},
  publisher    = {{Elsevier}},
  series       = {{Comptes Rendus Mathématique}},
  title        = {{Variational existence theory for hydroelastic solitary waves : Une théorie variationnelle d'existence d'ondes solitaires hydroélastiques}},
  url          = {{http://dx.doi.org/10.1016/j.crma.2016.10.004}},
  doi          = {{10.1016/j.crma.2016.10.004}},
  volume       = {{354}},
  year         = {{2016}},
}