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November  2003, 9(6): 1571-1586. doi: 10.3934/dcds.2003.9.1571

Modified wave operators for the coupled wave-Schrödinger equations in three space dimensions

Akihiro Shimomura 1,

1. 

Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

Received  October 2002 Revised  May 2003 Published  September 2003

We study the scattering theory for the coupled Wave-Schrödinger equation with the Yukawa type interaction, which is certain quadratic interaction, in three space dimensions. This equation belongs to the borderline between the short range case and the long range one. We construct modified wave operators for that equation for small scattered states with no restriction on the support of the Fourier transform of them.
Keywords: modified wave operators., long range scattering, asymptotic behavior of solutions, Wave-Schrödinger equations.
Mathematics Subject Classification: 35B40, 35P25, 35Q4.
Citation: Akihiro Shimomura. Modified wave operators for the coupled wave-Schrödinger equations in three space dimensions. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1571-1586. doi: 10.3934/dcds.2003.9.1571
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