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Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN

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Abstract

We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrödinger equation, including one-soliton solution, two-soliton solution, rogue wave solution, W-soliton solution and M-soliton solution. The prediction error for one-soliton, W-soliton and M-soliton is smaller. As the prediction distance increases, the prediction error will gradually increase. The unknown physical parameters of the high-order nonlinear Schrödinger equation are studied by using rogue wave solutions as data sets. The neural network is optimized from three aspects including the number of layers of the neural network, the number of neurons, and the sampling points. Compared with previous research, our error is greatly reduced. This is not a replacement for the traditional numerical method, but hopefully to open up new ideas.

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Acknowledgements

This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR20A050001), the National Natural Science Foundation of China (Grant Nos. 12075210 and 11874324) and the Scientific Research and Developed Fund of Zhejiang A&F University (Grant No. 2021FR0009).

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    1. College of Sciences, Zhejiang A&F University, Linan, 311300, Zhejiang, People’s Republic of China

      Yin Fang, Gang-Zhou Wu, Yue-Yue Wang & Chao-Qing Dai

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    1. Yin Fang
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    2. Gang-Zhou Wu
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    3. Yue-Yue Wang
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    4. Chao-Qing Dai
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    Correspondence to Yue-Yue Wang or Chao-Qing Dai.

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    Y. Fang and G. Z. Wu contributed equally to this work.

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    Fang, Y., Wu, GZ., Wang, YY. et al. Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN. Nonlinear Dyn 105, 603–616 (2021). https://doi.org/10.1007/s11071-021-06550-9

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