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

doi:10.1088/1361-6544/aad52c

	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
	2018-10-01
发表期刊	NONLINEARITY
ISSN	0951-7715
卷号	31 期号:10 页码:4746-4775
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.
关键词	Degasperis-Procesi equation multipeakons Toda lattice of CKP type
DOI	10.1088/1361-6544/aad52c
语种	英语
资助项目	National Natural Science Foundation of China ; [11701550] ; [11731014] ; [11331008] ; [11571358]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000444190100004
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30944
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.