Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes.

We study the dynamics of solutions of nonlinear Schrödinger equation (NLS) near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is proved. The novelty of our result is that we allow the existence of internal modes. [ABSTRACT FROM AUTHOR]