玻色-爱因斯坦凝聚体中涡旋团的出现和稳定性：线性极限附近的分歧方法
Emergence and Stability of Vortex Clusters in Bose-Einstein Condensates: a Bifurcation Approach near the Linear Limit
摘要：
研究了玻色-爱因斯坦凝聚体中交替电荷涡旋团簇的存在性和稳定性。它示出了这样的状态出现从级联的非线性断裂分岔，可以通过弱非线性少模扩展的线性极限附近的系统进行分析跟踪。我们提出了产生的状态，出现在线性极限的前几个特征值附近，并说明如何分叉的性质可以用来理解它们的稳定性。直线形、多边形和对角形涡旋团只是其中的一部分，而由暗孤子和涡旋团组成的混合态也被识别出来。
英文摘要：
We study the existence and stability properties of clusters of alternating charge vortices in Bose-Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well.
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