Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons,breathers, and rogue waves |
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Authors: | Zijian Zhou Zhenya Yan |
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Institution: | 1.Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | The dimensionless third-order nonlinear Schrödinger equation (alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g. bright soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated (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 bright solitons. |
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Keywords: | third-order nonlinear Schrödinger equation deep learning data-driven solitons data-driven parameter discovery |
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