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On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations

  • Scipio CuccagnaEmail author
  • Tetsu Mizumachi
Article

Abstract

We consider nonlinear Schrödinger equations
$$iu_t +\Delta u +\beta (|u|^2)u=0\, ,\, \text{for} (t,x)\in \mathbb{R}\times \mathbb{R}^d,$$
where d ≥ 3 and β is smooth. We prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t → ∞ assuming the so called the Fermi Golden Rule (FGR) hypothesis. We improve the “sign condition” required in a recent paper by Gang Zhou and I.M.Sigal.

Keywords

Soliton Solitary Wave Asymptotic Stability Energy Space Discrete Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.DISMI University of Modena and Reggio EmiliaReggio EmiliaItaly
  2. 2.Faculty of MathematicsKyushu UniversityHigashi-ku, FukuokaJapan

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