Аңдатпа
Spontaneous vortex nucleation is a universal feature of open and nonlinear physical systems. We investigate theoretically vortex rings and vortex lines emerging during propagation of self-trapped wave beams in nonlocal nonlinear media. We demonstrate how radially perturbed fundamental solitons exhibit extremely robust and long-lived oscillations with the spontaneous generation of a regular set of vortex rings at the wave beam periphery. We find numerically a class of cylindrically symmetric higher-order spatial solitons and investigate their stability and nonlinear dynamics. The formation of external vortex rings, similar to fundamental soliton, is accompanied by emergence of additional internal vortex-antivortex pairs nucleating from the edge-ring phase dislocation of perturbed higher-order soliton.