Time-dependent method for non-linear Schrödinger equations in inverse scattering problems

We consider an inverse scattering problem for a non-linear Schrödinger equation with a non-linearity of power-type. Applying the time-dependent technique, developed by Enss and Weder, we prove that the non-linearity is uniquely determined from a scattering data defined via the scattering operator. We also obtain a reconstruction formula which is valid for large scattering data.