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Stable and oscillating solitons of \(\pmb {\mathcal {PT}}\)-symmetric couplers with gain and loss in fractional dimension

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Abstract

Families of coupled solitons of \(\mathcal {PT}\)-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM) are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained \(\mathcal {PT}\)-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating \(\mathcal {PT}\)-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.

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Acknowledgements

We thank Dumitru Mihalache and Jiawei Li for their help on improving the writing of the manuscript.

Funding

This work was supported by National Major Instruments and Equipments Development Project of National Natural Science Foundation of China (No. 61827815), by National Natural Science Foundation of China (No. 62075138), and by Science and Technology Project of Shenzhen (Nos. JCYJ20190808121817100 and JCYJ20190808164007485).

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  1. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China

    Liangwei Zeng, Xiaowei Lu, Yi Cai, Qifan Zhu, Hongyi Chen, Hu Long & Jingzhen Li

  2. Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, College of Physics and Optoelectronics Engineering, Shenzhen University, Shenzhen, 518060, China

    Liangwei Zeng, Xiaowei Lu, Yi Cai, Qifan Zhu, Hongyi Chen, Hu Long & Jingzhen Li

  3. State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an, 710119, China

    Jincheng Shi

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Zeng, L., Shi, J., Lu, X. et al. Stable and oscillating solitons of \(\pmb {\mathcal {PT}}\)-symmetric couplers with gain and loss in fractional dimension. Nonlinear Dyn 103, 1831–1840 (2021). https://doi.org/10.1007/s11071-020-06180-7

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