Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning

• URL: http://arxiv.org/abs/2012.09984v1
• Date: Fri, 18 Dec 2020 00:09:21 GMT
• Title: Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
• Authors: Li Wang, Zhenya Yan
• Abstract summary: We use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schr"odinger (NLS) equation with the time-dependent potential. Results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.
• Score: 7.400475825464313
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schr\"odinger (NLS) equation with the time-dependent potential by considering several initial conditions such as the rogue wave, Jacobi elliptic cosine function, two-Gaussian function, or three-hyperbolic-secant function, and periodic boundary conditions. Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution. These results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.

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