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Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions
Chen, Xiao-Min1,2; Chang, Xiang-Ke1,2; Sun, Jian-Qing3; Hu, Xing-Biao1; Yeh, Yeong-Nan4
2015-07-01
Source PublicationNONLINEARITY
ISSN0951-7715
Volume28Issue:7Pages:2279-2306
AbstractIn this paper, we present a generalized Toeplitz determinant solution for the generalized Schur flow and propose a mixed form of the two known relativistic Toda chains together with its generalized Toeplitz determinant solution. In addition, we also give a Hankel type determinant solution for a nonisospectral Toda lattice. All these results are obtained by technical determinant operations. As a bonus, we finally obtain some new combinatorial numbers based on the moment relations with respect to these semi-discrete integrable systems and give the corresponding combinatorial interpretations by means of the lattice paths.
Keywordgeneralized determinant solutions combinatorial interpretations semi-discrete integrable system orthogonal polynomials
DOI10.1088/0951-7715/28/7/2279
Language英语
Funding ProjectNational Natural Science Foundation of China[11331008] ; National Natural Science Foundation of China[11371251] ; Knowledge Innovation Program of LSEC ; Shandong Provincial Natural Science Foundation, China[ZR2013AQ024] ; Institute of Computational Mathematics, AMSS, CAS
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000357106000011
PublisherIOP PUBLISHING LTD
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20133
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, AMSS, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing, Peoples R China
3.Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China
4.Acad Sinica, Inst Math, Taipei 115, Taiwan
Recommended Citation
GB/T 7714
Chen, Xiao-Min,Chang, Xiang-Ke,Sun, Jian-Qing,et al. Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions[J]. NONLINEARITY,2015,28(7):2279-2306.
APA Chen, Xiao-Min,Chang, Xiang-Ke,Sun, Jian-Qing,Hu, Xing-Biao,&Yeh, Yeong-Nan.(2015).Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions.NONLINEARITY,28(7),2279-2306.
MLA Chen, Xiao-Min,et al."Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions".NONLINEARITY 28.7(2015):2279-2306.
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