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The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning

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  • Zhang, Yabin
  • Wang, Lei
  • Zhang, Peng
  • Luo, Haotian
  • Shi, Wanlin
  • Wang, Xin

Abstract

We apply the deep learning approach to learn some nonlinear wave solutions of the Lakshmanan-Porsezian-Daniel (LPD) model characterizing the evolution of ultrashort optical pulse in optical fibers. Based on the strong universal approximation theorem, we give the initial-boundary value data and residual collocation points, choose the parameters initialization Xavier method and parameters optimization Adam and L-BFGS algorithms to construct the optimal neural network model. Then, we derive the data-driven solutions of the rogue wave, anti-dark soliton, multi-peak soliton, non-rational W-shaped soliton, rational W-shaped soliton as well as periodic-wave solutions for the LPD model. Finally, we study the parameters discovery of such model via the anti-dark soliton solution with 1% perturbation (or without perturbation).

Suggested Citation

  • Zhang, Yabin & Wang, Lei & Zhang, Peng & Luo, Haotian & Shi, Wanlin & Wang, Xin, 2022. "The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003654
    DOI: 10.1016/j.chaos.2022.112155
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    References listed on IDEAS

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    1. Wu, Gang-Zhou & Fang, Yin & Wang, Yue-Yue & Wu, Guo-Cheng & Dai, Chao-Qing, 2021. "Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    Cited by:

    1. Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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