Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes

doi:10.1016/j.physleta.2022.128373

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	Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes
	Zhou, Zijian 1,2; Wang, Li 3,4,5; Yan, Zhenya 1,2
	2022-10-31
发表期刊	PHYSICS LETTERS A
ISSN	0375-9601
卷号	450 页码:15
摘要	We introduce a deep neural network learning scheme to discover the Backlund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively. The first deep learning scheme takes advantage of some solution (or soliton equation) informations to train the data-driven BT discovery, and is valid in the study of the BT of the sine-Gordon equation, and complex and real Miura transforms between the defocusing (focusing) mKdV equation and KdV equation, as well as the data-driven mKdV equation discovery via the Miura transforms. The second deep learning scheme uses the higher-order solitons generated by the explicit/implicit BTs to study the data-driven discoveries of mKdV and sine-Gordon equations, in which the high-order soliton informations are more powerful for the enhanced leaning soliton equations with higher accuracies. (C) 2022 Elsevier B.V. All rights reserved.
关键词	Deep neural networks B?cklund transform Miura transform Soliton equations Breathers Solitons
DOI	10.1016/j.physleta.2022.128373
收录类别	SCI
语种	英语
资助项目	National Natural Science Foun- dation of China (NSFC)[11925108]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000869433000001
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/60783
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 3.Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China 4.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China 5.Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Zijian,Wang, Li,Yan, Zhenya. Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes[J]. PHYSICS LETTERS A,2022,450:15.
APA	Zhou, Zijian,Wang, Li,&Yan, Zhenya.(2022).Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes.PHYSICS LETTERS A,450,15.
MLA	Zhou, Zijian,et al."Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes".PHYSICS LETTERS A 450(2022):15.