On The large Time Asymptotics of Klein-Gordon type equations with General Data

Abstract

We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (non-radial) data. We prove that global solutions are asymptotically given by 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,SW2022}. This work generalizes the results of part of \cite{Liu-Sof1,Liu-Sof2} on the Schrödinger equation to arbitrary dimension, and non-radial data.