Exact vortex solitons in a quasi-two-dimensional Bose–Einstein condensate with spatially inhomogeneous cubic–quintic nonlinearity

Highlights: ► We propose some exact vortex soliton solutions of the Gross–Pitaevskii equation with spatially inhomogeneous cubic–quintic nonlinearity. ► We show that both attractive cubic–quintic nonlinearity and attractive cubic plus repulsive quintic nonlinearities support exact vortex solitons. ► The number of ring structures in the vortex solitons increases by one with increasing the radial quantum number by one. -- Abstract: The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the "radial quantum number" m by one.