Scattering Theory for the Coupled Klein-Gordon-SchrÃ¶dinger Equations in Two Space Dimensions

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Scattering Theory for the Coupled Klein-Gordon-SchrÃ¶dinger Equations in Two Space Dimensions

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 4, Page 661--685.

Shimomura, Akihiro
Scattering Theory for the Coupled Klein-Gordon-SchrÃ¶dinger Equations in Two Space Dimensions
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We study the scattering theory for the coupled Klein-Gordon-SchrÃ¶dinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state.

Mathematics Subject Classification (2000): 35B40, 35P25, 35Q40

Mathematical Reviews Number: MR2037763

Received: 2003-07-08

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