Stabilization of high-order solutions of the cubic nonlinear Schrödinger equation.

In this paper we consider the stabilization of nonfundamental unstable stationary solutions of the cubic nonlinear Schrödinger equation. Specifically, we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones, we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible.