Long Range Scattering and Modified Wave Operators for the WaveSchr"odinger system
Abstract
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular the existence of modified wave operators for that system with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.The method consists in solving the wave equation, substituting the result into the Schr"odinger equation,which then becomes both nonlinear and nonlocal in time,and treating the latter by the method previously used for a family of generalized Hartree equations with long range interactions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2001
 arXiv:
 arXiv:math/0107087
 Bibcode:
 2001math......7087G
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 35P25 (Primary) 35B40;
 35Q40;
 81U99 (Secondary)
 EPrint:
 LateX, 88 pages, available http://qcd.th.upsud.fr