  We present a new family of stationary solutions to the cubic nonlinear
Schroedinger equation with a Jacobian elliptic function potential. In the limit
of a sinusoidal potential our solutions model a dilute gas Bose-Einstein
condensate trapped in a standing light wave. Provided the ratio of the height
of the variations of the condensate to its DC offset is small enough, both
trivial phase and nontrivial phase solutions are shown to be stable. Numerical
simulations suggest such stationary states are experimentally observable.
