Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities

Abstract

We demonstrate that fractional cubic-quintic nonlinear Schr\"odinger equation,characterized by its L\'evy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital angular momentum. They can be built, in the respective optical setting, as circular chains of fundamental solitons linked by a vortical phase field. We predict semi-analytically that the metastable necklace-shaped clusters persist, corresponding to a local minimum of an effective potential of interaction between adjacent solitons in the cluster. Systematic simulations corroborate that the clusters stay robust over extremely large propagation distances, even in the presence of strong random perturbations.