Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities

TL;DR

This paper explores the formation and stability of ring-shaped soliton clusters, called necklaces, in fractional nonlinear Schrödinger equations with competing nonlinearities, demonstrating their robustness and metastability.

Contribution

It introduces a novel class of metastable soliton necklaces supported by fractional diffraction and nonlinearities, with semi-analytical predictions and extensive simulations confirming their stability.

Findings

Necklace-shaped soliton clusters persist as local minima of interaction potential.

Clusters remain robust over large propagation distances.

Strong perturbations do not destabilize the necklaces.

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.