Dynamics of solitons in non-homogeneous media

PDE Seminar
Tuesday, January 19, 2010 - 3:05pm for 1 hour (actually 50 minutes)
Skiles 255
Michael I. Weinstein – Columbia University
Zhiwu Lin
I will discuss the intermediate and long time dynamics of solutions of the nonlinear Schroedinger - Gross Pitaevskii equation, governing nonlinear dispersive waves in a spatially non-homogeneous background. In particular, we present results (with B. Ilan) on solitons with frequencies near a spectral band edge associated with periodic potential, and results (with Z. Gang) on large time energy distribution in systems with multiple bound states. Finally, we discuss how such results can inform strategies for control of soliton-like states in optical and quantum systems.