Bose-Einstein condensates in standing waves: The cubic nonlinear Schrodinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schr odinger equation with an elliptic function potential. In the limit of a sin usoidal potential our solutions model a quasi-one-dimensional dilute gas Bo se-Einstein condensate trapped in a standing light wave. Provided that the ratio of the height of the variations of the condensate to its de offset is , small enough, both trivial phase and nontrivial phase solutions are shown to he stable. Recent developments allow for experimental investigation of these predictions.