Variational existence theory for hydroelastic solitary waves

• Main Authors: Groves, Mark D., Hewer, Benedikt, Wahlén, Erik
• Format: Text
• Language: unknown
• Published: arXiv 2016
• Subjects: Analysis of PDEs math.AP; Mathematical Physics math-ph; Pattern Formation and Solitons nlin.PS; FOS Mathematics; FOS Physical sciences; 76B15 Primary 76B25, 74B20, 74F10, 35A15, 35R35 Secondary; Ice Sheet
• Online Access: https://dx.doi.org/10.48550/arxiv.1604.04459; https://arxiv.org/abs/1604.04459

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