A New Paradigm For Scattering Theory of Linear And Nonlinear Waves: Review And Open Problem

2024/08/26 by Soffer, Avy · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2408.14269

Abstract

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems, along with their significance and potential future applications in scattering and inverse scattering.

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• Weakly localized states of one dimensional Schrodinger equations have localized energy

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