Applied Maths Seminar: Stephane Lafortune -- Stability of persisting periodic solutions to a complex Ginzburg-Landau perturbation of NLS

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.