Stable vortex solitons of (2+1)(2+1)-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities

Applying the similarity transformation, two classes of vortex solitons are constructed in (2+1)(2+1)-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities, including the exact ones in the anharmonic potential and numerical ones in the harmonic potential. The properties of vortex solitons which are defined by the radial quantum number n and topological charge S are studied. The linear stability analysis and numerical simulation are used to verify the stability of these vortex solitons. The results show that stable vortex solitons exist for high radial quantum number and topological charge, within some region of values of chemical potential μ.

► Exact vortex solitons in cubic–quintic Gross–Pitaevskii equation with radially nonlinearity coefficients and anharmonic or harmonic potential are constructed.
► The stability of the vortex solitons are investigated by means of linear stability analysis and numerical simulation.
► The results show that stable vortex solitons exist for high radial quantum number and topological charge.