Stable manifolds for an orbitally unstable NLS

Abstract

We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.

This is a revised version of a paper that was originally posted in May. In this new version, the spectral assumptions have been changed. Only the generic ones remain. Also, there is a new Theorem 2 that establishes the existence of a codimension one stable manifold

References in corpus (3)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• Asymptotic stability of N-soliton states of NLS
• Global Strichartz estimates for nontrapping perturbations of the Laplacian

Cited by in corpus (20)

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• Stable manifolds for all monic supercritical NLS in one dimension
• A weighted estimate for two dimensional Schrodinger, matrix schrodinger and wave equations with resonance of first kind at zero energy
• Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD
• A Critical Centre-Stable Manifold for the Cubic Focusing Schroedinger Equation in Three Dimensions
• Spectral Theory and Nonlinear PDE: a Survey
• Count of eigenvalues in the generalized eigenvalue problem
• A Critical Centre-Stable Manifold for Schroedinger's Equation in R^3
• Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states
• Endpoint Strichartz Estimates for Charge Transfer Hamiltonians
• Spectra of Linearized Operators for NLS Solitary Waves
• Exponential decay of eigenfunctions and generalized eigenfunctions of a non self-adjoint matrix Schrödinger operator related to NLS
• Dispersive estimates using scattering theory for matrix Hamiltonian equations
• A class of stable perturbations for a minimal mass soliton in three dimensional saturated nonlinear Schrödinger equations
• Stability of solitary manifold near critical solitary wave