2012 Fiscal Year Final Research Report
Research on systems of the biorthogonal functions, discrete andultradiscrete integrable systems, and their applications
| Project/Area Number |
22540224
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Yoshimasa 京都大学, 大学院・情報学研究科, 教授 (50172458)
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| Co-Investigator(Renkei-kenkyūsha) |
KATO Tsuyoshi 京都大学, 大学院・情報学研究科, 教授 (20273427)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 可積分系 |
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| Research Abstract |
By using the theory of orthogonal polynomials and the theory of Hirota’s tau-functions, we study the system of bi-orthogonal functions with the help of the classical orthogonal functions and the nonautonomous discrete integrable systems. In this study, we have succeeded in deriving the discrete integrable systems associated with skew-orthogonal polynomials and making clear the relationship between the Padeinterpolations and the solutions of the elliptic Painleve equations in terms of elliptic hypergeometric functions. A stable numerical algorithm for the generalized eigenvalue problem of a tri-diagonal matrix pencil is introduced from the nonautonomous discrete integrable systems related to the classical biorthogonal rational functions.
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