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-Hao1,2; Zhao, Jun-Xiao2,3
刊名ADVANCES IN MATHEMATICS
2018-11-07
卷号338页码:1077-1118
关键词Multipeakons Pfaffian Novikov equation Toda lattice of BKP type
ISSN号0001-8708
DOI10.1016/j.aim.2018.09.023
英文摘要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.
资助项目National Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358] ; [11271362]
WOS研究方向Mathematics
语种英语
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号WOS:000447961200024
内容类型期刊论文
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/31655]  
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.
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