标题： 玻色气体的稳定性分析：外部势场和三体相互作用的影响以及在汤克斯-吉拉德 regimes 下的广义 Gross-Pitaevskii 方程 显示英文标题

标题： Stability analysis of Bose Gas: effect of external trapping and three-body interaction with Gross-Pitaevskii equation in Tonks-Girardeau regimes

摘要： 在这项工作中，我们研究了五次Gross-Pitaevskii（GP）方程在外部囚禁势存在和不存在的情况下，玻色气体（BG）在Tonks-Girardeau（TG）和超Tonks-Girardeau（sTG）区域的稳定性问题。为此，我们在散射长度存在的条件下，对该纯五次GP方程进行了解析和数值计算。利用时变变分方法，我们推导出两种情况下的运动方程和有效势能。通过有效势能，我们讨论了纯五次GP方程的稳定性性质，并获得了BECs的调制不稳定条件。变分结果通过使用分裂步Crank-Nicolson方法进行直接数值模拟得到验证，观测结果与解析预测一致。 显示英文摘要

摘要： In this work, we investigate the stability aspects of quintic Gross-Pitaevskii (GP) equation with the presence and absence of external trapping potential for a Bose Gas (BG) in both the Tonks-Girardeau (TG) and the super Tonks-Girardeau (sTG) regimes. For this purpose, we compute both analytically and numerically a pure quintic GP equation with the presence of the scattering lengths. Using the time-dependent variational approach, we derive the equations of motion and effective potential of the system for both cases. Through the effective potential, we discuss the stability properties of pure quintic GP equation and obtain the modulational instability condition of BECs. The variational results are verified by means of direct numerical simulations using split-step Crank-Nicolson method and the observed results are in agreement with the analytical predictions.