Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates

Effective wave equations that described axial dynamics of a Bose condensate confined in a external potential with cylindrical symmetry were derived. The three dimensional Gross-Pitaevskii equation and a variational approach was used for the study. The derived nonpolynomial Schrödinger equations were applied to model cigar-shaped and disc-shaped Bose condensates. Results were found in agreement with those of 3-D Gross-Pitaevskii equation for ground state and the dynamics of the condensate.