Abstract

We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, to the best of our knowledge, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent $\alpha$, becoming effectively long range at small $\alpha$ values. At long distance, it can be shown that this coupling decreases faster than exponentially: $\sim\exp (- |{\textbf{n}}|)/\sqrt {|n|}$. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower power levels, as the $\alpha$ coefficient diminishes, independently of their topological charge and/or pattern distribution.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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