The properties of 3D Bose–Einstein condensate have been studied with variational and numerical methods. In the variational approach, we use the super-Gaussian trial function, and it is demonstrated that this trial function is a good approach for providing the descriptions of the quantum droplets. The analytical equations for the variational parameters are obtained. The frequency of small oscillations of quantum droplets near the equilibrium position is estimated. It is also found that periodic modulation of the coupling constants leads to resonance oscillations of the quantum droplets parameters or emission of waves depending on the amplitude of the modulations. The predictions are supported by direct numerical simulation of the governing equation.

中文翻译：

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三维玻色-爱因斯坦凝聚体中的量子液滴

已经用变分和数值方法研究了 3D 玻色-爱因斯坦凝聚体的性质。在变分方法中，我们使用超高斯试验函数，证明该试验函数是提供量子液滴描述的好方法。获得了变分参数的解析方程。估计平衡位置附近量子液滴的小振荡频率。还发现耦合常数的周期性调制导致量子液滴参数的共振振荡或波的发射，这取决于调制的幅度。这些预测得到控制方程的直接数值模拟的支持。