Fractional discrete vortex solitons (2020)
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, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent α, becoming effectively long-range at small α values. At long-distance, it can be shown that this coupling decreases faster than exponential: ∼ exp(−|n|)/ p |n|. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower power levels, as the α coefficient diminishes, independently of their topological charge and/or pattern distribution.