Stabilization of higher-order vortices and multi-hump solitons in media with synthetic nonlocal nonlinearities

We address the evolution of higher-order excited states, such as vortex and multi-hump solitons, in nonlocal media with synthetic, competing focusing and defocusing nonlinearities with different nonlocal transverse scales. We reveal that introduction of suitable competing effects makes possible the stabilization of vortex solitons with topological charge m>2, as well as one-dimensional multi-hump solitons with number of humps p>4, all of which are highly unstable in natural nonlocal materials with focusing nonlinearities.