On a single class of vortex solutions of nonlinear Schrodinger equation

This work presents a detailed studying one of invariant solutions of Schrodinger equation with cubic nonlinearity. We obtain this solution through the methods of group analysis of differential equations. The analysis of behavior of integral curves of the factor system representing the system of three ordinary differential equations is performed. Both analytical and numerical methods are used.
The existence of periodical solutions for particular parameter value is proved. It is shown that in other cases all system trajectories tend asymptotically to some curve in the phase space. This curve, in its turn, is a trajectory for some value of parameter.