二维 Gross-Pitaevskii 方程中具有一阶系统的 Bogomol'nyi-Prasad-Sommerfield 界
A Bogomol'nyi-Prasad-Sommerfield bound with a first-order system in the $2D$ Gross-Pitaevskii equation
AI总结：
本文提出了二维 Gross-Pitaevskii 方程的新颖 BPS 界，证明其由满足两个一阶偏微分方程的系统饱和，并给出了环形区域中分数涡度构型的首批解析实例。
摘要：
本文提出了二维空间中 Gross-Pitaevskii 方程的一个新颖的 Bogomol'nyi-Prasad-Sommerfield (BPS) 界。能量可以从下方通过两个边界项的组合来界定，其中一个与涡度相关（但被凝聚体轮廓“修饰”），第二个与构型的“偏度”相关。该界由满足包含两个一阶偏微分方程的系统的构型所饱和。当这样的 BPS 系统被满足时，Gross-Pitaevskii 方程也同时被满足。本手稿中该 BPS 系统的解析解表示存在于环形区域中的具有分数涡度的构型。利用这些技术，我们给出了此类构型的首批解析实例。本文还讨论了该 BPS 系统的流体动力学解释，并概述了这些结果的意义。
英文摘要：
A novel Bogomol'nyi-Prasad-Sommerfield (BPS) bound for the Gross-Pitaevskii equations in two spatial dimensions is presented. The energy can be bounded from below in terms of the combination of two boundary terms, one related to the vorticity (but ``dressed'' by the condensate profile) and the second to the ``skewness'' of the configurations. The bound is saturated by configurations that satisfy a system of two first-order partial differential equations. When such a BPS system is satisfied, the Gross-Pitaevskii equations are also satisfied. The analytic solutions of this BPS system in the present manuscript represent configurations with fractional vorticity living in an annulus. Using these techniques, we present the first analytic examples of this kind. The hydrodynamical interpretation of the BPS system is discussed, and the implications of these results are outlined.
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