Quasilinear dynamics in nonlinear Schroedinger equations

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

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

Date: 12/12/2008

Time: 3:35pm - 4:25pm