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Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with PT-symmetric nonlinear lattices

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  • Su, Weiwei
  • Deng, Hanying
  • Dong, Liangwei
  • Huang, Zhenfen
  • Huang, Changming

Abstract

We investigate the existence and stability of fundamental solitons in the focusing nonlinear fractional Schrödinger equation with PT-symmetric nonlinear lattices. We show that in sharp contrast to the linear PT-symmetric lattice where stable fundamental solitons can be found only at a lower gain-loss level, PT-symmetric nonlinear lattices can support them at a higher gain-loss parameter. The localized profile of a fundamental soliton becomes narrower with an increase in the propagation constant or a decrease in the Lévy index. The velocity of the power-flow vector of fundamental solitons at a small propagation constant is faster than that with a large propagation constant. We also reveal that the stability region of fundamental solitons increases with the growth of the Lévy index. As the gain-loss level is increased, the stable domain can be extended with an increased propagation constant. These stability results were obtained by linear stability analysis and numerical simulations. The excitations of robust nonlinear fundamental states in the nonlinear fractional Schrödinger equation with PT-symmetric nonlinear lattices are studied as well.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308201
    DOI: 10.1016/j.chaos.2020.110427
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    References listed on IDEAS

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    1. Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Symmetry breaking of spatial Kerr solitons in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. 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).
    3. 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).
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