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

Akihiro Shimomura

doi:10.3934/dcds.2003.9.1571

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2003, Volume 9, Issue 6: 1571-1586. Doi: 10.3934/dcds.2003.9.1571

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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

Received: September 30, 2002

Revised: April 30, 2003

Published: October 2003

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Abstract

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.

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Mathematics Subject Classification: 35B40, 35P25, 35Q40.

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