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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 (2016) In Comptes Rendus Mathematique 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
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Comptes Rendus Mathematique
volume
354
issue
11
pages
9 pages
publisher
Editions scientifiques Elsevier
external identifiers
  • scopus:84994123732
  • wos:000388360700006
ISSN
1631-073X
DOI
10.1016/j.crma.2016.10.004
language
English
LU publication?
yes
id
f6487d0b-dbeb-4f62-9a58-49d32f165d86
date added to LUP
2016-11-21 09:54:56
date last changed
2017-09-18 11:30:54
@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    = {Editions scientifiques Elsevier},
  series       = {Comptes Rendus Mathematique},
  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},
  volume       = {354},
  year         = {2016},
}