Hermite-Pade approximations with Pfaffian structures: Novikov peakon equation and integrable lattices

doi:10.1016/j.aim.2022.108338

	Hermite-Pade approximations with Pfaffian structures: Novikov peakon equation and integrable lattices
	Chang, Xiang-Ke 1,2
刊名	ADVANCES IN MATHEMATICS
	2022-06-25
卷号	402 页码:45
关键词	Hermite-Pade approximation Biorthogonal polynomials Novikov equation Multipeakons
ISSN号	0001-8708
DOI	10.1016/j.aim.2022.108338
英文摘要	Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite-Pade approximation whose unique solution is a sequence of polynomials constructed with the help of Pfaffians. These polynomials belong to the family of recently proposed partial-skew-orthogonal polynomials. The relevance of partial-skew-orthogonal polynomials is especially visible in the approximation problem germane to the Novikov peakon problem so that we obtain explicit inverse formulae in terms of Pfaffians by reformulating the inverse spectral problem for the Novikov multipeakons. Furthermore, we investigate two Hermite-Pade approximations for the related spectral problem of the discrete dual cubic string, and show that these approximation problems can also be solved in terms of partial-skew-orthogonal polynomials and nonsymmetric Cauchy biorthogonal polynomials. This formulation results in a new correspondence among several integrable lattices. (c) 2022 Elsevier Inc. All rights reserved.
资助项目	National Natural Science Founda-tion of China[12171461] ; National Natural Science Founda-tion of China[11688101] ; National Natural Science Founda-tion of China[11731014] ; Youth Innovation Promotion Association CAS[2019004]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000793475900022
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61369]
专题	中国科学院数学与系统科学研究院
通讯作者	Chang, Xiang-Ke
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Box 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. Hermite-Pade approximations with Pfaffian structures: Novikov peakon equation and integrable lattices[J]. ADVANCES IN MATHEMATICS,2022,402:45.
APA	Chang, Xiang-Ke.(2022).Hermite-Pade approximations with Pfaffian structures: Novikov peakon equation and integrable lattices.ADVANCES IN MATHEMATICS,402,45.
MLA	Chang, Xiang-Ke."Hermite-Pade approximations with Pfaffian structures: Novikov peakon equation and integrable lattices".ADVANCES IN MATHEMATICS 402(2022):45.