Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices

doi:10.1007/s00332-021-09690-9

	Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices
	Chang, Xiang-Ke 2,3; Li, Shi-Hao 1; Tsujimoto, Satoshi 5; Yu, Guo-Fu 4
刊名	JOURNAL OF NONLINEAR SCIENCE
	2021-03-05
卷号	31 期号:2 页码:23
关键词	Two-parameter Cauchy two-matrix model Toda-type lattice Gram determinant technique
ISSN号	0938-8974
DOI	10.1007/s00332-021-09690-9
英文摘要	In this article, we consider the generalised two-parameter Cauchy two-matrix model and the corresponding integrable lattice equation. It is shown that with parameters chosen as 1/k(i), k(i) is an element of Z(>0) (i = 1, 2), the average characteristic polynomials admit (k(1)+ k(2)+ 2)-term recurrence relations, which can be interpreted as spectral problems for integrable lattices. The tau function is then given by the partition function of the generalised Cauchy two-matrix model as well as Gram determinant. The simplest solvable example is given.
资助项目	National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11731014] ; National Natural Science Foundation of China[11701550] ; National Natural Science Foundation of China[11871336] ; Youth Innovation Promotion Association CAS ; ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) ; JSPS KAK-ENHI[19H01792] ; JSPS KAK-ENHI[17K18725]
WOS研究方向	Mathematics ; Mechanics ; Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000626523300001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58330]
专题	中国科学院数学与系统科学研究院
通讯作者	Yu, Guo-Fu
作者单位	1.Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, POB 2719, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China 5.Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Yoshida Honmachi, Kyoto 6068501, Japan
推荐引用方式 GB/T 7714	Chang, Xiang-Ke,Li, Shi-Hao,Tsujimoto, Satoshi,et al. Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices[J]. JOURNAL OF NONLINEAR SCIENCE,2021,31(2):23.
APA	Chang, Xiang-Ke,Li, Shi-Hao,Tsujimoto, Satoshi,&Yu, Guo-Fu.(2021).Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices.JOURNAL OF NONLINEAR SCIENCE,31(2),23.
MLA	Chang, Xiang-Ke,et al."Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices".JOURNAL OF NONLINEAR SCIENCE 31.2(2021):23.