Small localized data in H^4000 for the 3D Klein-Gordon-Schrödinger system produce global solutions that decay and scatter to free waves.
Baillon and John M
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Large Time Behavior of the Klein-Gordon-Schr\"{o}dinger system
Small localized data in H^4000 for the 3D Klein-Gordon-Schrödinger system produce global solutions that decay and scatter to free waves.