Variational existence theory for hydroelastic solitary waves
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 establis...
| Main Authors: | , , |
|---|---|
| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2016
|
| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.1604.04459 https://arxiv.org/abs/1604.04459 |
| 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 ${\mathcal E}$ subject to the constraint ${\mathcal I}=2μ$, where ${\mathcal I}$ is the horizontal impulse and $0< μ\ll 1$, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions of he nonlinear Schrödinger equation with cubic focussing nonlinearity as $μ\downarrow 0$. : As accepted for publication |
|---|