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We suggest a simple Gaussian Lagrangian variational scheme for the reducedtime-dependent quasi-one- and quasi-two-dimensional Gross-Pitaevskii (GP)equations of a dipolar Bose-Einstein condensate (BEC) in cigar and diskconfigurations, respectively. The variational approximation for stationarystates and breathing oscillation dynamics in reduced dimensions agrees wellwith the numerical solution of the GP equation even for moderately largeshort-range and dipolar nonlinearities. The Lagrangian variational scheme alsoprovides much physical insight about soliton formation in dipolar BEC.

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions