Stephane Lafortune College of Charleston Stability of persisting periodic solutions to a complex Ginzburg-Landau perturbation of NLS Wednesday 25th July 14:05-14:55pm, Eastern Avenue Lecture Theatre. It was shown in [Cruz-Pacheco, Levermore, and Luce (2004)] that some periodic solutions to the nonlinear Shrodinger equation (NLS) persist when the NLS is subject to a perturbation leading to the Complex Ginzburg Landau equation (CGL). In this presentation, I will show how one can use methods coming from the theory of integrability together with the Evans function to study the spectral stability of these persisting solutions. In particular I show that the solutions of NLS are spectrally stable with respect to periodic perturbations. However, the solutions can become unstable when NLS is perturbed to CGL.