2022/04/24 by Avy Soffer, Xiaoxu Wu, Soffer, Avy +1
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2204.11261
openalex publication_date 2022/04/24 · openalex created_date 2022/04/28 · openalex updated_date 2026/07/28
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 \citeLiu-Sof1,Liu-Sof2,SW2020,SW2022. This work generalizes the results of part of \citeLiu-Sof1,Liu-Sof2 on the Schrödinger equation to arbitrary dimension, and non-radial data.