Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type

doi:10.1088/1361-6544/aad52c

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
	Chang, Xiang-Ke1,2 ; Hu, Xing-Biao1,2 ; Li, Shi-Hao 1,2
刊名	NONLINEARITY
	2018-10-01
卷号	31 期号:10 页码:4746-4775
关键词	Degasperis-Procesi equation multipeakons Toda lattice of CKP type
ISSN号	0951-7715
DOI	10.1088/1361-6544/aad52c
英文摘要	In 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.
资助项目	National Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000444190100004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30955]
专题	计算数学与科学工程计算研究所
通讯作者	Chang, Xiang-Ke
作者单位	1.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
推荐引用方式 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.