On the large time asymptotics of Schrödinger type equations with general data

For the Schrödinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutions are asymptotically given by the sum of a free wave and a weakly localized part. The proof is based on constructing in an adapted way the Free Channel Wave Operator, and further tools from the recent works [21,22,35] . This work generalizes the results of the first part of [21,22] to arbitrary dimension, and non-radial data.