We consider nonlinear Schr\"odinger 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
On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations / Cuccagna, Scipio; T., Mizumachi. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 284:(2008), pp. 51-77. [10.1007/s00220-008-0605-3]
On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations
CUCCAGNA, Scipio;
2008
Abstract
We consider nonlinear Schr\"odinger 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
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