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

文献类型：期刊论文

作者Zhou, Zijian2,3; Wang, Li1,4,5; Yan, Zhenya2,3
刊名PHYSICS LETTERS A
出版日期2022-10-31
卷号450页码:15
关键词Deep neural networks B?cklund transform Miura transform Soliton equations Breathers Solitons
ISSN号0375-9601
DOI10.1016/j.physleta.2022.128373
英文摘要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.
资助项目National Natural Science Foun- dation of China (NSFC)[11925108]
WOS研究方向Physics
语种英语
WOS记录号WOS:000869433000001
出版者ELSEVIER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60782]  
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.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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