Stability of exact solutions of the defocusing nonlinear Schrodinger equation with periodic potential in two dimensions

Abstract

The cubic nonlinear Schrodinger equation with repulsive nonlinearity and elliptic function potential in two-dimensions models a repulsive dilute gas Bose--Einstein condensate in a lattice potential. A family of exact stationary solutions is presented and its stability is examined using analytical and numerical methods. All stable trivial-phase solutions are off-set from the zero level. Our results imply that a large number of condensed atoms is sufficient to form a stable, periodic condensate.Comment: 12 pages, Latex, High resolution version available at http://www.amath.washington.edu/~kutz/research.htm