Vortex solitons in Bose–Einstein condensates with inhomogeneous attractive nonlinearities and a trapping potential

We demonstrate three-dimensional (3D) vortex solitary waves in the (3+1)D nonlinear Gross–Pitaevskii equation (GPE) with spatially modulated nonlinearity and a trapping potential. The analysis is carried out in spherical coordinates, providing for novel localized solutions, and the 3D vortex solitary waves are built that depend on three quantum numbers. Our analytical findings are corroborated by a direct numerical integration of the original equations. It is demonstrated that the vortex solitons found are stable for the quantum numbers n ≤ 2 , l ≤ 2 and m = 0 , 1 , independent of the propagation distance.