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 Schrodinger equation with an elliptic function potential. In the limit of a sinusoidal potential our solutions model a quasi-one-dimensional dilute gas Bose-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.