On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations
نویسندگان
چکیده
We consider nonlinear Schrödinger equations iut +∆u+ β(|u| )u = 0 , for (t, x) ∈ R × R, 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 Fermi Golden Rule (FGR) hypothesis. We improve the “sign condition”required in a recent paper by Gang Zhou and I.M.Sigal.
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