We study the dilute and ultracold unitary Bose gas, which is characterized by a universal equation of state due to the diverging s-wave scattering length, under a transverse harmonic confinement. From the hydrodynamic equations of superfluids we derive an effective one-dimensional nonpolynomial Schrodinger equation (1D NPSE) for the axial dynamics which, however, takes also into account the transverse dynamics. Finally, by solving the 1D NPSE we obtain meaningful analytical formulas for the dark (gray and black) solitons of the bosonic system.

中文翻译：

---

幺正玻色气体中的暗孤子

我们研究了在横向谐波限制下由于发散 s 波散射长度而具有通用状态方程的稀释和超冷单一 Bose 气体。从超流体的流体动力学方程我们推导出一个有效的一维非多项式薛定谔方程 (1D NPSE) 轴向动力学，然而，它也考虑了横向动力学。最后，通过求解一维 NPSE，我们获得了玻色系统的暗（灰色和黑色）孤子的有意义的解析公式。