 Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearityPengfei Li, Boris A. Malomed and Dumitru Mihalache Chaos, Solitons & Fractals, 2020, vol. 137, issue C Abstract: We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schrödinger equation (NLSE) with competing cubic-quintic nonlinearities and the Lévy index (fractionality) taking values 1 ≤ α ≤ 2. Families of ring-shaped VSs with vorticities s=1,2, and 3 are constructed in a numerical form. Unlike the usual two-dimensional NLSE (which corresponds to α=2), in the fractional model VSs exist above a finite threshold value of the total power, P. Stability of the VS solutions is investigated for small perturbations governed by the linearized equation, and corroborated by direct simulations. Unstable VSs are broken up by azimuthal perturbations into several fragments, whose number is determined by the fastest growing eigenmode of small perturbations. The stability region, defined in terms of P, expands with the increase of α from 1 up to 2 for all s=1, 2, and 3, except for steep shrinkage for s=2 in the interval of 1 ≤ α ≤ 1.3. Keywords: Vortex soliton; Nonlinear Schrödinger equation; Lévy index; Competing cubic-quintic nonlinearities (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920301855 DOI: 10.1016/j.chaos.2020.109783 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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