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 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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