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Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices

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Abstract

We show that vector solitons can be stable in nonlinear fractional Schrödinger equations with one-dimensional parity-time-symmetric optical lattices. The families of vector solitons with two propagation constants that are present in the different gaps are investigated. It is found that the Lévy index cannot change the phase transition point, but it will influence the solitons existence and stability. The effective widths of the two vector soliton components shrink as the Lévy index decreases. Some unique soliton propagation properties are found, and soliton propagation simulations are performed to authenticate the results of the stability analyses.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 11774068 and 61675001), the Guangdong Province Nature Science Foundation of China (Grant No. 2017A030311025), the Guangdong Province Education Department Foundation of China (Grant No. 2014KZDXM059), and the Guangzhou Institute of International Finance (Grant No. 16GFR02B07).

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Authors and Affiliations

  1. School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou, 510521, China

    Jiaquan Xie

  2. School of Photoelectric Engineering, Guangdong Polytechnic Normal University, Guangzhou, 510665, China

    Xing Zhu & Yingji He

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  1. Jiaquan Xie
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Correspondence to Xing Zhu.

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Xie, J., Zhu, X. & He, Y. Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices. Nonlinear Dyn 97, 1287–1294 (2019). https://doi.org/10.1007/s11071-019-05048-9

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