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Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
Zhou, Zijian1,2; Yan, Zhenya1,2
2021-01-28
发表期刊PHYSICS LETTERS A
ISSN0375-9601
卷号387页码:12
摘要In this paper, we investigate the logarithmic nonlinear Schrodinger (LNLS) equation with the parity-time (PT)-symmetric harmonic potential, which is an important physical model in many fields such as nuclear physics, quantum optics, magma transport phenomena, and effective quantum gravity. Three types of initial value conditions and periodic boundary conditions are chosen to solve the LNLS equation with PT-symmetric harmonic potential via the physics-informed neural networks (PINNs) deep learning method, and these obtained results are compared with ones deduced from the Fourier spectral method. Moreover, we also investigate the effectiveness of the PINNs deep learning for the LNLS equation with PT symmetric potential by choosing the distinct space widths or distinct optimized steps. Finally, we use the PINNs deep learning method to effectively tackle the data-driven discovery of the LNLS equation with PT-symmetric harmonic potential such that the coefficients of dispersion and nonlinear terms or the amplitudes of PT-symmetric harmonic potential can be approximately found. (C) 2020 Elsevier B.V. All rights reserved.
关键词Logarithmic nonlinear Schrodinger equation PT-symmetric potentials Physics-informed neural networks Deep learning Data-driven discovery of LNLS equation Data-driven solitons
DOI10.1016/j.physleta.2020.127010
收录类别SCI
语种英语
资助项目NSFC[11731014] ; NSFC[11925108]
WOS研究方向Physics
WOS类目Physics, Multidisciplinary
WOS记录号WOS:000593454400007
出版者ELSEVIER
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/57796
专题中国科学院数学与系统科学研究院
通讯作者Yan, Zhenya
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
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GB/T 7714
Zhou, Zijian,Yan, Zhenya. Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning[J]. PHYSICS LETTERS A,2021,387:12.
APA Zhou, Zijian,&Yan, Zhenya.(2021).Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning.PHYSICS LETTERS A,387,12.
MLA Zhou, Zijian,et al."Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning".PHYSICS LETTERS A 387(2021):12.
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