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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 517395, 7 pages
http://dx.doi.org/10.1155/2013/517395
Research Article

A Time-Splitting and Sine Spectral Method for Dynamics of Dipolar Bose-Einstein Condensate

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received 28 May 2013; Accepted 9 July 2013

Academic Editor: Fedele Lizzi

Copyright © 2013 Si-Qi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A two-component Bose-Einstein condensate (BEC) described by two coupled a three-dimension Gross-Pitaevskii (GP) equations is considered, where one equation has dipole-dipole interaction while the other one has only the usual s-wave contact interaction, in a cigar trap. The time-splitting and sine spectral method in space is proposed to discretize the time-dependent equations for computing the dynamics of dipolar BEC. The singularity in the dipole-dipole interaction brings significant difficulties both in mathematical analysis and in numerical simulations. Numerical results are given to show the efficiency of this method.