Stabilizing two-dimensional solitons in a Kerr cavity

Summary form only given. In two transverse dimensions radially symmetric eigenmodes of the nonlinear Schrodinger equation (NLS) typically collapse to a catastrophic self-focus. In this paper we show that a Kerr medium in a driven dissipative cavity can support stable 2-D solitons, and we consider stabilization of the unstable solitons by control-of-chaos methods. We use the mean-field Kerr cavity model for a self-focusing Kerr medium.