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 a new way the Free Channel Wave Operator, and further tools from the recent works \cite{Liu-Sof1,Liu-Sof2,SW2020}. This work generalizes the results of the first part of \cite{Liu-Sof1,Liu-Sof2} to arbitrary dimension, and non-radial data.

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