Inverse problem for stationary state of a Bose-Einstein condensate

The Bose-Einstein condensate is generally described by the three-dimensional equations. However, the two-dimensional case is of great interest too. First, these results can be directly used to study the planar condensates [1]. Second, it serves as a test version for numerical calculations and as a quasi-two-dimensional approximation for the complete three-dimensional problem. An additional advantage of the two-dimensional case is that with the help of variational approach one can obtain analytical results for the stationary state and for the expansion of the condensate [2].