An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type

doi:10.1016/j.aim.2018.09.023

	An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
	Chang, Xiang-Ke1,2 ; Hu, Xing-Biao1,2 ; Li, Shi-Hao 1,2; Zhao, Jun-Xiao 2,3
	2018-11-07
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	338 页码:1077-1118
摘要	The Novikov equation is an integrable analogue of the Camassa-Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this paper, an approach involving Pfaffians is applied to study multipeakons of the Novikov equation. First, we show that the Novikov peakon ODEs describe an isospectral flow on the manifold cut out by certain Pfaffian identities. Then, a link between the Novikov peakons and the finite Toda lattice of BKP type (B-Toda lattice) is established based on the use of Pfaffians. Finally, certain generalizations of the Novikov equation and the finite B-Toda lattice are proposed together with special solutions. To our knowledge, it is the first time that the peakon problem is interpreted in terms of Pfaffians. (C) 2018 Elsevier Inc. All rights reserved.
关键词	Multipeakons Pfaffian Novikov equation Toda lattice of BKP type
DOI	10.1016/j.aim.2018.09.023
语种	英语
资助项目	National Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358] ; [11271362]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000447961200024
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31656
专题	计算数学与科学工程计算研究所
通讯作者	Li, Shi-Hao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, POB 2719, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Glasgow Int Coll, 56 Dumbarton Rd, Glasgow G11 6NU, Lanark, Scotland
推荐引用方式 GB/T 7714	Chang, Xiang-Ke,Hu, Xing-Biao,Li, Shi-Hao,et al. An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type[J]. ADVANCES IN MATHEMATICS,2018,338:1077-1118.
APA	Chang, Xiang-Ke,Hu, Xing-Biao,Li, Shi-Hao,&Zhao, Jun-Xiao.(2018).An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type.ADVANCES IN MATHEMATICS,338,1077-1118.
MLA	Chang, Xiang-Ke,et al."An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type".ADVANCES IN MATHEMATICS 338(2018):1077-1118.