Two-dimensional solitons in a Kerr cavity

We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.