Expansion of Bose-Einstein condensates in lower dimensions

In the hydrodynamic approximation we obtain analytic solutions to the Gross-Pitaevskii equation with positive scattering length which describe expansions of the Bose-Einstein condensates in quasi-one and quasi-two dimensional geometries. The expansion laws are expressed in terms of the initial sizes of the condensate and the trap frequencies before release, that is in terms of experimentally measurable parameters only. Three-dimensional effects are estimated with the use of variational approach. The analytical formulae show good agreement with available experimental data.