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arXiv · 1604.04459

Variational existence theory for hydroelastic solitary waves

Mark D. Groves·Benedikt Hewer·Erik Wahlén
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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 $\gamma$. We establish the existence of a minimiser of the wave energy ${\mathcal E}$ subject to the constraint ${\mathcal I}=2\mu$, where ${\mathcal I}$ is the horizontal impulse and $0< \mu \ll 1$, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions of he nonlinear Schr\"{o}dinger equation with cubic focussing nonlinearity as $\mu \downarrow 0$.

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BibTeXRIS

Mark D. Groves, Benedikt Hewer, Erik Wahlén. 2016-04-15. Variational existence theory for hydroelastic solitary waves. https://doi.org/10.1016/j.crma.2016.10.004

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