Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation

We investigate stability of (2 + 1)-dimensional ring solitons of the nonlin ear Schrodinger equation with focusing cubic and defocusing quintic nonline arities. Computing eigenvalues of the linearised equation, we show that rin gs with spin (topological charge) s = 1 and s = 2 are linearly stable, prov ided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally res olve a controversial stability issue for this class of models. (C) 2001 Els evier Science B.V. All rights reserved.