Speaker
Mariana Haragus, University of Franche-Comté
Abstract
The dynamics of periodic waves is well understood for dissipative systems, whereas for dispersive equations most existing stability results show that periodic waves are orbitally stable within the class of solutions which have the same period and spectrally stable/unstable when general bounded perturbations are considered. The focus of this talk is on the nonlinear dynamics of spectrally stable periodic waves for an NLS-type equation with damping, detuning and driving which arises in nonlinear optics. We consider localized perturbations and subharmonic perturbations, i.e., periodic perturbations with period equal to an integer multiple of the period of the wave.
These are joint works with M. Johnson, W. Perkins and B. de Rijk.