# Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator

@article{Komech2007GlobalWF,
title={Global well-posedness for the Schr{\"o}dinger equation coupled to a nonlinear oscillator},
author={Alexander Komech and Andrew Komech},
journal={Russian Journal of Mathematical Physics},
year={2007},
volume={14},
pages={164-173}
}
• Published 31 August 2006
• Mathematics
• Russian Journal of Mathematical Physics
The Schrödinger equation with the nonlinearity concentrated at a single point proves to be an interesting and important model for the analysis of long-time behavior of solutions, including asymptotic stability of solitary waves and properties of weak global attractors. In this note, we prove global well-posedness of this system in the energy space H1.
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