Quasilinear dynamics in nonlinear Schroedinger equations
Speaker: Vadim Zharnitsky, University of Illinois at Urbana-Champaign
Abstract: We describe a new scenario of an almost linear behavior in strongly nonlinear systems. This phenomenon is demonstrated for the cubic one dimensional nonlinear Schroedinger equation with periodic boundary conditions, where we have nearly complete understanding of the phenomenon. The nonlinearity gets ``averaged out'' by the high frequency solutions and this leads to an averaging type theorem for PDEs. We will also briefly discuss the application of this phenomenon in the field of nonlinear optics. This is joint work with M. Burak Erdogan.
Room Reservation Information
Room Number: 106 McAllister
Time: 3:35pm - 4:25pm