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Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity

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  • Li, Pengfei
  • Malomed, Boris A.
  • Mihalache, Dumitru

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.

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  • Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920301855
    DOI: 10.1016/j.chaos.2020.109783
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    References listed on IDEAS

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    1. Caplan, R.M. & Carretero-González, R. & Kevrekidis, P.G. & Malomed, B.A., 2012. "Existence, stability, and scattering of bright vortices in the cubic–quintic nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1150-1171.
    2. Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Symmetry breaking of spatial Kerr solitons in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Zhang, Li & He, Yingji, 2020. "Soliton dynamics in a fractional complex Ginzburg-Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. Li, S.R. & Bao, Y.Y. & Liu, Y.H. & Xu, T.F., 2022. "Bright solitons in fractional coupler with spatially periodical modulated nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Zeng, Liangwei & Mihalache, Dumitru & Malomed, Boris A. & Lu, Xiaowei & Cai, Yi & Zhu, Qifan & Li, Jingzhen, 2021. "Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Zeng, Liangwei & Belić, Milivoj R. & Mihalache, Dumitru & Wang, Qing & Chen, Junbo & Shi, Jincheng & Cai, Yi & Lu, Xiaowei & Li, Jingzhen, 2021. "Solitons in spin-orbit-coupled systems with fractional spatial derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Zeng, Liangwei & Zeng, Jianhua, 2020. "Fractional quantum couplers," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Su, Weiwei & Deng, Hanying & Dong, Liangwei & Huang, Zhenfen & Huang, Changming, 2020. "Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with PT-symmetric nonlinear lattices," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Zeng, Liangwei & Belić, Milivoj R. & Mihalache, Dumitru & Zhu, Xing, 2024. "Elliptical and rectangular solitons in media with competing cubic–quintic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    7. dos Santos, Mateus C.P., 2024. "Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    8. Dong, Liangwei & Du, Zhijing & Ren, Zhijun, 2023. "Fractional angular momentum borne on rotating vortex solitons," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    9. He, Shangling & Malomed, Boris A. & Mihalache, Dumitru & Peng, Xi & Yu, Xing & He, Yingji & Deng, Dongmei, 2021. "Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    10. Bai, Xiaoqin & Bai, Juan & Malomed, Boris A. & Yang, Rongcao, 2024. "Spectrum conversion and pattern preservation of Airy beams in fractional systems with a dynamical harmonic-oscillator potential," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    11. Liu, Dongshuai & Gao, Yanxia & Fan, Dianyuan & Zhang, Lifu, 2023. "Higher-charged vortex solitons in harmonic potential," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. Wang, Qing & Zhang, Lingling & Ke, Lin, 2022. "Parameters controlling of vortex solitons in nonlocal nonlinear medium with gradually characteristic length," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    13. Zeng, Liangwei & Zhu, Yongle & Malomed, Boris A. & Mihalache, Dumitru & Wang, Qing & Long, Hu & Cai, Yi & Lu, Xiaowei & Li, Jingzhen, 2022. "Quadratic fractional solitons," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    14. Kudryashov, Nikolay A., 2020. "Optical solitons of model with integrable equation for wave packet envelope," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    15. Wang, Qing & Zhang, Lingling & Malomed, Boris A. & Mihalache, Dumitru & Zeng, Liangwei, 2022. "Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation by means of Lévy-index management," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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