2001 Fiscal Year Final Research Report Summary
Studies on the orthogonal polynomials, the continued fractions and the discrete integrable systems
| Project/Area Number |
12640121
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University (2001)
Osaka University (2000) |
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Principal Investigator |
TSUJIMOTO Satoshi Kyoto University, Graduate School of Informatics, Lecturer, 情報学研究科, 講師 (60287977)
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| Co-Investigator(Kenkyū-buntansha) |
KONDO Koichi Osaka University, Graduate School of Engineering Science, Research Assistant, 基礎工学研究科, 助手 (30314397)
NAGAI Atsushi Osaka University, Graduate School of Engineering Science, Research Assistant, 基礎工学研究科, 助手 (90304039)
NAKAMURA Yoshimasa Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (50172458)
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| Project Period (FY) |
2000 – 2001
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| Keywords | discrete integrable system / orthogonal polynomial / Toda equation / Lotka-Volterra equation / algorithm / eigen-value problem / identity of determinants / continued fractions |
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| Research Abstract |
In the last decades, discrete integrable system has been getting a lot of attention from the viewpoints of difference scheme and algorithm. Already there have been many discussions about relations between continuous-time integrable system and orthogonal polynomials. There are only a few studies on the relations between full-discretised (discrete time and space) systems and orthogonal polynomials fully clarified, such as the discrete integrable system (Toda, Lotka-Volterra) and classical orthogonal polynomials by Spiridonov and Zhedanov. Hence the purpose of this studies is to clarify the relations between the discrete integrable system and the orthogonal polynomials and to develop the Numerical algorithms related to the orthogonality. At first, we pick up the discrete hungry Lotka-Volterra equation and the coupled KP equation. We probe them by means of Hirota's tau-function and develop the relations.
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