Dark-soliton stripes on a paraboloidal background in a bulk nonlinear medium

We demonstrate self-similar evolution of fundamental and higher-order dark soliton stripes on a paraboloidal background in a bulk graded-index waveguide with self-defocusing nonlinearity. The results show that the dark soliton stripes can self-similarly evolve on the paraboloidal background when they pass through the nonlinear well or barrier, and their evolutions may lead to the generation of the optical vortex when the initial dark soliton stripes deviate from the central position of the paraboloidal background. In addition, the interactions between neighboring dark soliton stripes on the paraboloidal background are investigated, which exhibits some complicated vortex patterns.