KMS Of Academy of mathematics and systems sciences, CAS
| 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
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| 2018-11-07 | |
| Source Publication | ADVANCES IN MATHEMATICS
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| ISSN | 0001-8708 |
| Volume | 338Pages:1077-1118 |
| Abstract | 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. |
| Keyword | Multipeakons Pfaffian Novikov equation Toda lattice of BKP type |
| DOI | 10.1016/j.aim.2018.09.023 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358] ; [11271362] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000447961200024 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31656 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Li, Shi-Hao |
| Affiliation | 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 |
| Recommended Citation 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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