Abstract
We study the global existence and long-time behavior of solutions of the initial-value problem for the cubic nonlinear Schrödinger equation with an attractive localized potential and a time-dependent nonlinearity coefficient. For small initial data, we show under some nondegeneracy assumptions that the solution approaches the profile of the ground state and decays in time like t-1/4. The decay is due to resonant coupling between the ground state and the radiation field induced by the time-dependent nonlinearity coefficient.
Original language | English (US) |
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Pages (from-to) | 85-120 |
Number of pages | 36 |
Journal | Journal of Differential Equations |
Volume | 220 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2006 |
Externally published | Yes |
Keywords
- Asymptotic stability
- Ground states
- Nonlinear Schrödinger equation
- Parametric resonance
ASJC Scopus subject areas
- Analysis
- Applied Mathematics