Semiclassical Focusing Nonlinear Schrodinger Equation I: Inverse scattering map and its evolution for radiative initial data

We consider the semiclassical limit for the focusing nonlinear (cubic) Schrodinger Equation (NLS) in the pure radiational case. We present a method of reconstructing the leading order terms of the solitonless initial data and of its evolution for a wide class of the corresponding reflection coefficients