We study the long-time behavior of solutions of the nonlinear Schrödinger equation in one space dimension for initial conditions in a small neighborhood of a stable solitary wave. Under some hypothesis on the structure of the spectrum of the linearized operator, we prove that, asymptotically in time
✦ LIBER ✦
On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations
✍ Scribed by Scipio Cuccagna; Tetsu Mizumachi
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 388 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0010-3616
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## Abstract Local exact controllability of the one‐dimensional NLS (subject to zero‐boundary conditions) with distributed control is shown to hold in a __H__^1^‐neighbourhood of the nonlinear ground state. The __Hilbert Uniqueness Method__ (__HUM__), due to Lions, is applied to the linear control p