We introduce a nonlinear Schrödinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where $a{n}^{1/3}\ll 1$ with $a$ the interatomic $\mathit{s}$-wave scattering length and $n$ the bosonic density, to the unitarity limit, where $a\to +\infty$. We call this equation the unitarity Schrödinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

• Received 17 December 2007

DOI:https://doi.org/10.1103/PhysRevA.77.033618