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

Abstract

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.

12 pages, 6 figures

References in corpus (3)

• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
• Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning

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• Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network
• Predicting positon solutions of a family of Nonlinear Schrödinger equations through Deep Learning algorithm