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

TL;DR

This paper reviews recent advances in scattering theory for linear and nonlinear waves, highlighting a unified approach to various dispersive and hyperbolic equations, and discusses open problems and future research directions.

Contribution

It introduces a comprehensive review of a unified scattering theory framework applicable to diverse wave equations and identifies key open problems for future exploration.

Findings

Unified approach to dispersive and hyperbolic equations

Application to time-dependent potentials and nonlinear equations

Identification of open problems in scattering and inverse scattering

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.