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Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
Chang, Xiang-Ke1,2; Hu, Xing-Biao1,2; Li, Shi-Hao1,2
2018-10-01
Source PublicationNONLINEARITY
ISSN0951-7715
Volume31Issue:10Pages:4746-4775
AbstractIn this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa-Holm (CH) peakon dynamical system and the finite Toda lattice may be regarded as opposite flows in some sense. As an intriguing analogue to the CH equation, the Degasperis-Procesi (DP) equation also supports the presence of peakon solutions. Noticing that the peakon solution to the DP equation is expressed in terms of bimoment determinants related to the Cauchy kernel, we impose opposite time evolution on the moments and derive the corresponding bilinear equation. The corresponding quartic representation is shown to be a continuum limit of a reduced discrete CKP equation, due to which we call the obtained equation a finite Toda lattice of CKP type. Then, a nonlinear version of the C-Toda lattice together with a Lax pair is derived. As a result, it is shown that the DP peakon lattice and the finite C-Toda lattice form opposite flows under a certain transformation.
KeywordDegasperis-Procesi equation multipeakons Toda lattice of CKP type
DOI10.1088/1361-6544/aad52c
Language英语
Funding ProjectNational Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000444190100004
PublisherIOP PUBLISHING LTD
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30944
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, POB 2719, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Chang, Xiang-Ke,Hu, Xing-Biao,Li, Shi-Hao. Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type[J]. NONLINEARITY,2018,31(10):4746-4775.
APA Chang, Xiang-Ke,Hu, Xing-Biao,&Li, Shi-Hao.(2018).Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type.NONLINEARITY,31(10),4746-4775.
MLA Chang, Xiang-Ke,et al."Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type".NONLINEARITY 31.10(2018):4746-4775.
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