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Symmetry breaking of spatial Kerr solitons in fractional dimension

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

Abstract

We study symmetry breaking of solitons in the framework of a nonlinear fractional Schrödinger equation (NLFSE), characterized by its Lévy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric, and antisymmetric soliton solutions are found, with stable asymmetric soliton solutions emerging from unstable symmetric and antisymmetric ones by way of symmetry-breaking bifurcations. Two different bifurcation scenarios are possible. First, symmetric soliton solutions undergo a symmetry-breaking bifurcation of the pitchfork type, which gives rise to a branch of asymmetric solitons, under the action of the self-focusing nonlinearity. Second, a family of asymmetric solutions branches off from antisymmetric states in the case of self-defocusing nonlinearity through a bifurcation of an inverted-pitchfork type. Systematic numerical analysis demonstrates that increase of the Lévy index leads to shrinkage or expansion of the symmetry-breaking region, depending on parameters of the double-well potential. Stability of the soliton solutions is explored following the variation of the Lévy index, and the results are confirmed by direct numerical simulations.

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  • Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Symmetry breaking of spatial Kerr solitons in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077920300011
    DOI: 10.1016/j.chaos.2020.109602
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    References listed on IDEAS

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    1. 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).
    2. Mingkai Liu & David A. Powell & Ilya V. Shadrivov & Mikhail Lapine & Yuri S. Kivshar, 2014. "Spontaneous chiral symmetry breaking in metamaterials," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
    3. Albuch, Lior & Malomed, Boris A., 2007. "Transitions between symmetric and asymmetric solitons in dual-core systems with cubic–quintic nonlinearity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 312-322.
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    Cited by:

    1. Zeng, Liangwei & Zeng, Jianhua, 2020. "Fractional quantum couplers," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. 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).
    3. 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).
    4. 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).
    5. 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).
    6. 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).
    7. 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).
    8. Merabti, Abdelouahab & Triki, Houria & Azzouzi, Faiçal & Zhou, Qin & Biswas, Anjan & Liu, Wenjun & Alzahrani, Abdullah Kamis & EL-Akrmi, Abdessetar, 2020. "Propagation properties of chirped optical similaritons with dual-power law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. 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).

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