SMS scnews item created by Georg Gottwald at Fri 6 Jul 2007 1459
Type: Seminar
Distribution: World
Expiry: 25 Jul 2007
Calendar1: 25 Jul 2007 1405-1500
CalLoc1: Eastern Avenue Lecture Theatre
Auth: gottwald@p6363.pc.maths.usyd.edu.au

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.  


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