Sriburadet Sirilak, Shih Yin-Tzer, Jeng B-W, Hsueh C-H, Chien C-S
Department of Applied Mathematics, National Chung Hsing University, Taichung, 402, Taiwan.
Department of Mathematics Education, National Taichung University of Education, Taichung, 403, Taiwan.
Sci Rep. 2021 Nov 23;11(1):22801. doi: 10.1038/s41598-021-02249-4.
We study the existence of nontrivial solution branches of three-coupled Gross-Pitaevskii equations (CGPEs), which are used as the mathematical model for rotating spin-1 Bose-Einstein condensates (BEC). The Lyapunov-Schmidt reduction is exploited to test the branching of nontrivial solution curves from the trivial one in some neighborhoods of bifurcation points. A multilevel continuation method is proposed for computing the ground state solution of rotating spin-1 BEC. By properly choosing the constraint conditions associated with the components of the parameter variable, the proposed algorithm can effectively compute the ground states of spin-1 [Formula: see text] and [Formula: see text] under rapid rotation. Extensive numerical results demonstrate the efficiency of the proposed algorithm. In particular, the affect of the magnetization on the CGPEs is investigated.
我们研究了三耦合格罗斯 - 皮塔耶夫斯基方程（CGPEs）非平凡解分支的存在性，该方程被用作旋转自旋 - 1玻色 - 爱因斯坦凝聚体（BEC）的数学模型。利用李雅普诺夫 - 施密特约化来检验在分岔点的某些邻域内非平凡解曲线从平凡解曲线的分支情况。提出了一种多级延拓方法来计算旋转自旋 - 1玻色 - 爱因斯坦凝聚体的基态解。通过适当选择与参数变量分量相关的约束条件，所提出的算法能够有效地计算快速旋转下自旋 - 1 和 的基态。大量的数值结果证明了所提算法的有效性。特别地，研究了磁化对三耦合格罗斯 - 皮塔耶夫斯基方程的影响。
