Title:  Stability of Ground States for cubic NLS in 1-D

Abstract:  In this talk, we discuss orbital stability of ground state (equilibrium) solutions for a 1D cubic nonlinear focussing Schrödinger equation under perturbations of H1(R) initial data for cNLS. Stability of equilibrium solutions is an important condition for being able to use theoretical models in physical applications. The method of proof is a generalization of Lyapunov stability theory for nite dimensional systems. We rely on global time existence of a unique H1(R) solution to the cNLS (Ginibre-Velo, 1977).