Multisymplectic structure-preserving scheme for the coupled Gross-Pitaevskii equations
Multisymplectic structure-preserving scheme for the coupled Gross-Pitaevskii equations
复制标题
耦合 Gross-Pitaevskii 方程的多重辛结构保持格式
DOI：
10.1080/00207160.2020.1781100
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发表时间：
2021
影响因子：
1.8
通讯作者：
Wang Yushun
中科院分区：
文献类型：
--
作者：
Wang Lan;Wang Yushun
在本文中，我们对旋转玻色-爱因斯坦凝聚体（BEC）的动力学进行数值研究，该动力学模型是通过带有角动量旋转项的耦合格罗斯-皮塔耶夫斯基（CGP）方程建模的。首先，通过引入一些规范动量来研究 CGP 方程的多辛结构，这使得我们能够构造相应的多辛格式。然后在时间和空间方向上应用中点规则，为 CGP 方程提出了多辛格式。讨论了多重辛格式的保守性质和收敛性分析。截止函数技术用于误差估计。数值算例验证了其保守性和收敛速度。
In this paper, we study numerically the dynamics of the rotating Bose–Einstein condensates (BECs) modelled by the coupled Gross–Pitaevskii (CGP) equations with angular momentum rotating terms. First, the multisymplectic structure of the CGP equations is investigated by introducing some canonical momenta which allows us to construct the corresponding multisymplectic schemes. Then applying the midpoint rule in both temporal and spatial directions, a multisymplectic scheme is proposed for the CGP equations. The conservative properties and the convergence analysis are discussed for the multisymplectic scheme. The cut-off function technique is utilized for the error estimation. Numerical examples are carried out to verify the conservative property and the convergence rate.