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

Details Global well-posedness for the Schroedinger equation coupled to a nonlinear oscillator Global well-posedness for the Schroedinger equation coupled to a nonlinear oscillator

2006-08-31

arxiv.org/abs/math/0608780v3

Mathematics

Analysis of PDEs

11 pages

Scientific paper

10.1134/S1061920807020057

The Schroedinger 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, such as the 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 $H\sp 1$.

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