Multi-symplectic variational integrators for the Gross-Pitaevskii equations in BEC

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• 作者：Cuicui Liao^a ; ^{cliao@jiangnan.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wanqiang Shen^a ; ^{wq_shen@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xiaohua Ding^b ; ^{mathdxh@hit.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multi-symplectic form formula ; Variational integrator ; Conservation law ; Gross&ndash ; Pitaevskii equation ; Bose&ndash ; Einstein condensate
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：60
• 期：Complete
• 页码：120-125
• 全文大小：723 K

文摘

In this paper, a variational integrator is constructed for Gross–Pitaevskii equations in Bose–Einstein condensate. The discrete multi-symplectic geometric structure is derived. The discrete mass and energy conservation laws are proved. The numerical tests show the effectiveness of the variational integrator, and the performance of the proved discrete conservation law.