# Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves

arXiv: https://arxiv.org/abs/2104.14809 · HTML: https://mlsanity.com/paper/2104.14809/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 57 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems](https://mlsanity.com/paper/1809.08327/) (2018)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning](https://mlsanity.com/paper/2012.09984/) (2020)

## Built on by (most cited first, 4 of 4)

- [Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?](https://mlsanity.com/paper/2412.06158/) (2024)
- [Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemes](https://mlsanity.com/paper/2111.09489/) (2021)
- [Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons](https://mlsanity.com/paper/2112.14040/) (2021)
- [Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network](https://mlsanity.com/paper/2303.09133/) (2023)

## 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.