Mean Field Models of Bose-Einstein Condensates: From Instabilities to Waves, from Solitons to Patterns
by
Panayotis Kevrekidis
University of Massachusetts

In the past few years, Bose-Einstein condensation has become an exciting playground for nonlinear waves. Bright and dark solitons, vortices, wave trains and vortex lattices have become experimentally accessible in this novel setting of coherent matter waves. In this talk, we will focus on mean field models of such waves in the context of the Gross-Pitaevskii equation and its variants. We will highlight some of the instability mechanisms that lead to the formation of solitons and then we will focus on the nonlinear waves and the patterns consisting of trains or lattices of such coherent structures. When possible, we will give comparisons of analytical predictions and numerical findings with experimental results. We will conclude with a number of future challenges and open questions in this intriguing journey.

Date received: September 29, 2003