Fractional discrete vortex solitons

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, 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 exponential: $\sim \exp (-|\mathbf{n}|)/\sqrt{|\mathbf{n}|}$. 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.

arXiv comment15 pages, 4 figures

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Cited by in corpus (2)

• Localized modes in nonlinear fractional systems with deep lattices
• Solitons in Quasiperiodic Lattices with Fractional Diffraction