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.

12 pages, Latex, High resolution version available at http://www.amath.washington.edu/~kutz/research.html

Cited by in corpus (5)

• Bloch Waves and Bloch Bands of Bose-Einstein Condensates in Optical Lattices
• General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
• Analytical results for the superflow of spin-orbit-coupled Bose-Einstein condensates in optical lattices
• Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions
• Spatiotemporal Bloch states of a spin-orbit coupled Bose-Einstein condensate in an optical lattice