  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 $\mu
\downarrow 0$.
