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Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity

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  • Lashkin, Volodymyr M.
  • Cheremnykh, Oleg K.

Abstract

We study the fractional three-dimensional (3D) nonlinear Schrödinger equation with exponential saturating nonlinearity. In the case of the Levy index α=1.9, this equation can be considered as a model equation to describe strong Langmuir plasma turbulence. The modulation instability of a plane wave is studied, the regions of instability depending on the Lévy index, and the corresponding instability growth rates are determined. Numerical solutions in the form of 3D fundamental soliton (ground state) are obtained for different values of the Lévy index. It was shown that in a certain range of soliton parameters it is stable even in the presence of a sufficiently strong initial random disturbance, and the self-cleaning of the soliton from such initial noise was demonstrated.

Suggested Citation

  • Lashkin, Volodymyr M. & Cheremnykh, Oleg K., 2024. "Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008063
    DOI: 10.1016/j.chaos.2024.115254
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    References listed on IDEAS

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    1. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Peng, Xi & He, Yingji, 2020. "Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. 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).
    3. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
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