  We begin a study of a multi-parameter family of Cauchy initial-value problems
for the modified nonlinear Schr\"odinger equation, analyzing the solution in
the semiclassical limit. We use the inverse scattering transform for this
equation, along with the steepest descent method of Deift and Zhou. The initial
conditions are selected both to allow all relevant scattering data to be
calculated without approximation and also to place the governing equation in a
transsonic state in which the quantum fluid dynamical system formally
approximating it is of hyperbolic type for some $x$ and of elliptic type for
other $x$. Our main result is a global approximation theorem valid in a maximal
space-time region connected to the elliptic part of the initial data.
