Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

doi:10.1088/1674-1056/ac4cc5

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/ac4cc5

Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉)^†

School of Mathematics, South China University of Technology, Guangzhou 510640, China

收稿日期:2021-11-22 修回日期:2022-01-05 接受日期:2022-01-24 出版日期:2022-05-17 发布日期:2022-06-07
通讯作者: De-Lu Zeng E-mail:dlzeng@scut.edu.cn
基金资助:
Project supported by National Natural Science Foundation of China (Grant Nos. 11771151, 61571005, and 61901160), the Science and Technology Program of Guangzhou (Grant No. 201904010362), and the Fundamental Research Program of Guangdong Province, China (Grant No. 2020B1515310023).

Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉)^†

School of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2021-11-22 Revised:2022-01-05 Accepted:2022-01-24 Online:2022-05-17 Published:2022-06-07
Contact: De-Lu Zeng E-mail:dlzeng@scut.edu.cn
Supported by:
Project supported by National Natural Science Foundation of China (Grant Nos. 11771151, 61571005, and 61901160), the Science and Technology Program of Guangzhou (Grant No. 201904010362), and the Fundamental Research Program of Guangdong Province, China (Grant No. 2020B1515310023).

摘要/Abstract

摘要： Rogue waves are a class of nonlinear waves with extreme amplitudes, which usually appear suddenly and disappear without any trace. Recently, the parity-time ($\mathcal {PT}$)-symmetric vector rogue waves (RWs) of multi-component nonlinear Schrödinger equation ($n$-NLSE) are usually derived by the methods of integrable systems. In this paper, we utilize the multi-stage physics-informed neural networks (MS-PINNs) algorithm to derive the data-driven $\mathcal {PT}$ symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition. The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.

关键词: nonlinear Schrödinger equation, vector rogue waves, deep learning, numerical simulations

Abstract: Rogue waves are a class of nonlinear waves with extreme amplitudes, which usually appear suddenly and disappear without any trace. Recently, the parity-time ($\mathcal {PT}$)-symmetric vector rogue waves (RWs) of multi-component nonlinear Schrödinger equation ($n$-NLSE) are usually derived by the methods of integrable systems. In this paper, we utilize the multi-stage physics-informed neural networks (MS-PINNs) algorithm to derive the data-driven $\mathcal {PT}$ symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition. The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.

Key words: nonlinear Schrödinger equation, vector rogue waves, deep learning, numerical simulations

中图分类号: (Integrable systems)

02.30.Ik

02.60.Cb (Numerical simulation; solution of equations) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation[J]. 中国物理B, 2022, 31(6): 60201-060201.

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Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

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