Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning

doi:10.1016/j.physd.2021.133037

	Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
	Wang, Li ; Yan, Zhenya 1
刊名	PHYSICA D-NONLINEAR PHENOMENA
	2021-12-15
卷号	428 页码:15
关键词	Nonlinear dispersive equation Initial-boundary value conditions Physics-informed neural networks Deep learning Data-driven peakon and periodic peakon solutions Data-driven parameter discovery
ISSN号	0167-2789
DOI	10.1016/j.physd.2021.133037
英文摘要	In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves with discontinuous first-order derivative at the wave peak. In this paper, we apply the multi-layer physics-informed neural networks (PINNs) deep learning to successfully study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations with initial-boundary value conditions such as the Camassa-Holm (CH) equation, Degasperis-Procesi equation, modified CH equation with cubic nonlinearity, Novikov equation with cubic nonlinearity, mCH-Novikov equation, b-family equation with quartic nonlinearity, generalized modified CH equation with quintic nonlinearity, and etc. Moreover, we also study the data-driven parameter discovery of the CH equation with the aid of the single peakon These results will be useful to further study the peakon solutions and corresponding experimental design of nonlinear dispersive equations. (C) 2021 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[11925108] ; National Natural Science Foundation of China[11731014]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000715124100003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59549]
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	Wang, Li,Yan, Zhenya. Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning[J]. PHYSICA D-NONLINEAR PHENOMENA,2021,428:15.
APA	Wang, Li,&Yan, Zhenya.(2021).Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning.PHYSICA D-NONLINEAR PHENOMENA,428,15.
MLA	Wang, Li,et al."Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning".PHYSICA D-NONLINEAR PHENOMENA 428(2021):15.