Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
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Abstract (arXiv)
The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wave in plasma and the wave propagation of ultrashort light pulses in optical fibers, as well as broader-banded waves on deep water. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g., soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and unperturbated (a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of solitons.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 8 of its 57 references that are in the map. First posted on arXiv 30 Apr 2021.
Builds on
8 of 57 references.
References · 8
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- 2017Solving high-dimensional partial differential equations using deep learningcited by 549
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- 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
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- 2020Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learningcited by 12
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Citing papers per year: 2021: 2; 2022: 0; 2023: 1; 2024: 1.
4 papers.
- 2024Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?cited by 5
- 2021Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemescited by 1
- 2021Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitonscited by 0
- 2023Predicting nonlinear reshaping of periodic signals in optical fibre with a neural networkcited by 0
- 2024Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?9 Dec 2024
- 2023Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network16 Mar 2023
- 2021Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons28 Dec 2021
- 2021Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemes18 Nov 2021