Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning

doi:10.1016/j.physleta.2020.127010

	Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
	Zhou, Zijian 1,2; Yan, Zhenya 1,2
刊名	PHYSICS LETTERS A
	2021-01-28
卷号	387 页码:12
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
ISSN号	0375-9601
DOI	10.1016/j.physleta.2020.127010
英文摘要	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.
资助项目	NSFC[11731014] ; NSFC[11925108]
WOS研究方向	Physics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000593454400007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57795]
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
推荐引用方式 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.