Recent observations of droplets in dipolar and binary Bose–Einstein condensate (BEC) gives motivation to study the theory of droplet formation in detail. Specifically, the authors are interested in investigating the possibility of droplet formation in a quasi‐1D geometry. Recent observations have suggested that droplets are stabilized by competition between effective mean‐field and beyond mean‐field interaction. Hence, it is possible to map the effective equation of motion to a cubic‐quartic nonlinear Schrödinger equation (CQNLSE). Two analytical solutions of the modified Gross–Pitaevskii equation or CQNLSE are obtained and they are verified numerically. Based on their stability, the parameter regime for which droplets can form is investigated. The effective potential allows for conclusions about the regions of soliton domination and self‐bound droplet formations.

中文翻译：

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量子液滴研究：一种分析方法

最近在偶极和二元玻色-爱因斯坦冷凝液（BEC）中观察到的液滴为详细研究液滴形成理论提供了动力。特别是，作者有兴趣研究准一维几何形状中液滴形成的可能性。最近的观察表明，液滴通过有效均值场和超出均值场相互作用之间的竞争而稳定。因此，可以将有效的运动方程映射到三次四次非线性Schrödinger方程（CQNLSE）。获得了修正的Gross–Pitaevskii方程或CQNLSE的两个解析解，并进行了数值验证。基于它们的稳定性，研究了液滴可以形成的参数范围。