Variational existence theory for hydroelastic solitary waves

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 Schrödinger equation with cubic focussing nonlinearity as $\mu \downarrow 0$.

As accepted for publication

References in corpus (1)

• Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity

Cited by in corpus (1)

• Stability of Periodic Travelling Flexural-Gravity Waves in Two Dimensions