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Within the formalism of the Gross-Pitaevskii equation, we derive effectiveone- and two-dimensional equations for cigar- and pancake-shaped dipolarBose-Einstein condensates with arbitrary polarization angle. These are based onan ansatz for the condensate wavefunction whose width in the tightly-confineddirection/s is treated variationally. The equations constitute a coupledpartial differential for the low-dimensional wavefunction and algebraicequations for the width parameters. This approach accurately predicts theground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einsteincondensates, and gives strong agreement with the three-dimensional results,even as the trapping is relaxed away from the strict quasi-one- andquasi-two-dimensional regimes. This approach offers a significant improvementover the standard one- and two-dimensional reduction.

Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates