Title: Solitons with rings and vortex rings on solitons in nonlocal nonlinear media,
Abstract: Nonlocality is a key feature of many physical systems since it prevents a
catastrophic collapse and a symmetry-breaking azimuthal instability of intense
wave beams in a bulk self-focusing nonlinear media. This opens up an intriguing
perspective for stabilization of complex topological structures such as
higher-order solitons, vortex rings and vortex ring-on-line complexes. Using
direct numerical simulations, we find a class of cylindrically-symmetric $n$-th
order spatial solitons having the intensity distribution with a central bright
spot surrounded by $n$ bright rings of varying size. We investigate dynamical
properties of these higher-order solitons in a media with thermal nonlocal
nonlinear response. We show theoretically that a vortex complex of vortex ring
and vortex line, carrying two independent winding numbers, can be created by
perturbation of the stable optical vortex soliton in nonlocal nonlinear media.