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

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

Chaos, Solitons & Fractals, 2022, vol. 159, issue C

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).

Keywords: Deep learning; Data-driven solutions; Parameters discovery; Converted waves; Lakshmanan-Porsezian-Daniel model (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003654

DOI: 10.1016/j.chaos.2022.112155

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