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 (1)

• Asymptotic stability of N-soliton states of NLS

Cited by in corpus (3)

• Stable manifolds for all monic supercritical NLS in one dimension
• Spectral Theory and Nonlinear PDE: a Survey
• Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II