On The large Time Asymptotics of Schrödinger type equations with General Data

2022/03/01 by Avy Soffer, Xiaoxu Wu, Soffer, Avy +1 · 2 citations
Engineering · Mathematics · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2203.00724

openalex publication_date 2022/03/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

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 \citeLiu-Sof1,Liu-Sof2,SW2020. This work generalizes the results of the first part of \citeLiu-Sof1,Liu-Sof2 to arbitrary dimension, and non-radial data.

Cited by

• Weakly localized states of one dimensional Schrodinger equations have localized energy
• Construction of modified wave operators via wave packet transform

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