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Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials

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Abstract

Under parity-time symmetric potentials, different-order nonlinearities such as cubic, quintic and septimal nonlinearities, altogether with their combinations and second-order and fourth-order dispersions/diffractions are simultaneously considered to form three-dimensional optical solitons. Based on some high-order nonlinear Schrödinger equations, three-dimensional analytical optical soliton solutions are found. In the defocusing cubic nonlinear case, three-dimensional optical soliton without fourth-order diffraction/dispersion is stable than that with fourth-order diffraction/dispersion. However, in the defocusing cubic and focusing quintic nonlinear case, the stability situation of soliton is just on the contrary. Among all combinations of nonlinearity, the stability of three-dimensional optical soliton in the cubic-quintic nonlinear case is better than that in the cubic nonlinear case, but worse than that in the cubic-quintic-septimal nonlinear case. In the quintic-septimal nonlinear case, three-dimensional optical soliton is unstable and will collapse ultimately.

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Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F050011).

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Authors and Affiliations

  1. School of Sciences, Zhejiang A&F University, Lin’an, 311300, Zhejiang, People’s Republic of China

    Chao-Qing Dai, Yan Fan & Yue-Yue Wang

  2. Zhejiang Provincial Key Laboratory of Chemical Utilization of Forestry Biomass, Zhejiang A&F University, Lin’an, 31130, Zhejiang, People’s Republic of China

    Chao-Qing Dai, Yan Fan & Yue-Yue Wang

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  1. Chao-Qing Dai
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  2. Yan Fan
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  3. Yue-Yue Wang
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Correspondence to Chao-Qing Dai.

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Dai, CQ., Fan, Y. & Wang, YY. Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials. Nonlinear Dyn 98, 489–499 (2019). https://doi.org/10.1007/s11071-019-05206-z

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  • DOI: https://doi.org/10.1007/s11071-019-05206-z

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