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

Abstract

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 $H\sp 1$.

11 pages

References in corpus (3)

• Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field
• On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator
• On Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation

Cited by in corpus (5)

• The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit
• The point-like limit for a NLS equation with concentrated nonlinearity in dimension three
• On asymptotic stability of solitons for nonlinear Schödinger equation
• The 1-D Dirac equation with concentrated nonlinearity
• On Asymptotic Stability of Solitary Waves in Discrete Schrödinger Equation Coupled to Nonlinear Oscillator