Variational existence theory for hydroelastic solitary waves : Une théorie variationnelle d'existence d'ondes solitaires hydroélastiques
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...
| Published in: | Comptes Rendus Mathematique |
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| Main Authors: | , , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Elsevier
2016
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| Subjects: | |
| Online Access: | https://lup.lub.lu.se/record/f6487d0b-dbeb-4f62-9a58-49d32f165d86 https://doi.org/10.1016/j.crma.2016.10.004 |
| Summary: | 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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