Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger system II

TL;DR

This paper advances scattering theory for a coupled Schrödinger-wave system in three dimensions by removing previous restrictions on initial data and refining the asymptotic analysis of solutions.

Contribution

It introduces an improved asymptotic form for solutions, allowing the elimination of support restrictions on the asymptotic states in the scattering analysis.

Findings

Existence of modified wave operators without size restrictions.

Refined asymptotic description of solutions in the scattering regime.

Elimination of support condition on asymptotic states.

Abstract

We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for that system with no size restriction on the data and we determined the asymptotic behaviour in time of solutions in the range of the wave operators, under a support condition on the asymptotic state required by the different propagation properties of the wave and Schr"odinger equations.Here we eliminate that condition by using an improved asymptotic form for the solutions.