On asymptotic stability in energy space of ground states for Nonlinear Schrödinger equations

Abstract

We consider nonlinear Schrödinger equations in dimension 3 or higher. We prove that symmetric finite energy solutions close to orbitally stable ground states converge asymptotically to a sum of a ground state and a dispersive wave 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

References in corpus (8)

• Selection of the ground state for nonlinear Schroedinger equations
• Asymptotic stability of N-soliton states of NLS
• Asymptotic stability of small solitons to 1D NLS with potential
• On instability of excited states of the nonlinear Schrödinger equation
• Asymptotic stability of small solitons for 2D Nonlinear Schrödinger equations with potential
• Dispersion for Schrödinger equation with periodic potential in 1D
• On asymptotic stability of solitons for nonlinear Schödinger equation
• Relaxation of Solitons in Nonlinear Schrodinger Equations with Potential

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