The Dynamical Systems seminar is held on Monday afternoons at
4:00 PM in CCDS 548 . There will be a brief tea in CCDS 548 at 3:45PM.
January 27th Björn de Rijk (KIT)
Title: Orbital stability of spatially periodic waves in the Klein-Gordon equation against localized perturbations
Abstract:
Nonlinear stability for spatially periodic waves in dispersive systems has so far been obtained against co-periodic or subharmonic perturbations by leveraging the Hamiltonian structure or other conserved quantities. However, nonlinear stability against localized perturbations remains largely unexplored. Since the perturbed wave is neither periodic nor localized in this case, the usual conservation laws are unavailable, thus obstructing a standard nonlinear stability argument. In this talk, I present a nonlinear orbital stability result for spatially periodic waves in the Klein-Gordon equation against $L^2$-localized perturbations. This is joint work with Emile Bukieda and Louis Garénaux.
Abstract: