Vortex solitons under competing nonlocal cubic and local quintic nonlinearities

Abstract

Vortex solitons in nonlinear media with competing nonlocal self-focusing cubic and local self-defocusing quintic nonlinearities are studied analytically and numerically. By using an approximate variational approach, we obtain bifurcated solutions of the vortex solitons with the upper (lower) branch carrying larger (smaller) power stemmed by the competing effect between cubic and quintic nonlinearities. Besides the better stability of vortex solitons due to the competing effect, similar to the dynamics of the vortex solitons in the media with single nonlocal cubic nonlinearity only, the vortex solitons located in the lower branch always split into multipole scalar solitons in the limit of weak nonlocality and propagate stably when the degree of nonlocality is sufficiently strong. On the other hand, the internal modes of the vortex solitons in the upper branch are always unstable, and will break up into rings or spots of particle clusters. The dynamics and the stability of the vortex solitons are numerically demonstrated with the split-step Fourier transform method.