Static vortex solutions for particles system situated on a plane and submitting to the generalized Pauli principle

One studies systems of particles on a plane subordinating to the Pauli generalized principle. In terms of approximation of mean field the system is described by the Schroedinger equation with complex nonlinearity. Within such a system the number of particles, total energy and angular moment are reserved. One studies vortex-shaped stationary configurations of ψ(r) ρ(r)1/2einθ type and writes down the Fokker-Plank differential equation governing the shape of vortex. One found the analytical solution of that equation and derived closed expression for vortex profile. One studies some average characteristics of the system, in particular, calculates energy spectrum and angular moment of vortex