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Abundant vector soliton prediction and model parameter discovery of the coupled mixed derivative nonlinear Schrödinger equation

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Abstract

Using the extended physics-informed neural network with twin subnets to study the coupled mixed derivative nonlinear Schrödinger equation (NLSE), seven types of vector solitons including vector single soliton, vector double solitons, anti-dark vector single soliton, anti-dark vector double solitons, vector rogue wave, vector bright–dark single soliton and vector bright–dark double solitons are predicted. The prediction results from seven types of vector solitons with different angles confirm that the physical neural network can be used to effectively solve the coupled mixed derivative NLSE. The error on the two sides and the falling point of the vector rogue wave solution is significantly greater than the middle, while the error of other six types of vector soliton solution mainly reflects in the peak or valley value of bright or dark soliton, and increases along the transmission distance. In addition, how to improve the prediction of model parameters from two aspects of data set and loss function is also studied. These results have certain reference value for studying the optical soliton transmission process by the machine learning.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

Zhejiang Provincial Natural Science Foundation of China (Grant No. LR20A050001); National Natural Science Foundation of China (Grant Nos. 12075210 and 12261131495); the Scientific Research and Developed Fund of Zhejiang A&F University (Grant No. 2021FR0009); and the National Training Programs of Innovation and Entrepreneurship for Undergraduates of China (Grant No. 202210341025).

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Authors and Affiliations

  1. College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, 311300, Lin’an, China

    Xue-Kun Wen, Jun-Hang Jiang, Wei Liu & Chao-Qing Dai

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  1. Xue-Kun Wen
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  2. Jun-Hang Jiang
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  3. Wei Liu
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  4. Chao-Qing Dai
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Correspondence to Wei Liu or Chao-Qing Dai.

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Wen, XK., Jiang, JH., Liu, W. et al. Abundant vector soliton prediction and model parameter discovery of the coupled mixed derivative nonlinear Schrödinger equation. Nonlinear Dyn 111, 13343–13355 (2023). https://doi.org/10.1007/s11071-023-08531-6

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  • DOI: https://doi.org/10.1007/s11071-023-08531-6

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