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

  • Scipio CuccagnaEmail author
  • Tetsu Mizumachi


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.


Soliton Solitary Wave Asymptotic Stability Energy Space Discrete Mode 
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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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