2010 Fiscal Year Final Research Report
Theory of Painleve systems and its new development
| Project/Area Number |
19340039
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
KAJIWARA Kenji Kyushu University, 数理学研究院, 教授 (40268115)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAI Tomoyuki 九州大学, 大学院・数理学研究院, 教授 (70302932)
IWASAKI Katsunori 北海道大学, 大学院・理学研究院, 教授 (00176538)
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| Co-Investigator(Renkei-kenkyūsha) |
NOUMI Masatoshi 神戸大学, 大学院・理学研究科, 教授 (80164672)
YAMADA Yasuhiko 神戸大学, 大学院・理学研究科, 教授 (00202383)
SAKAI Hidetaka 東京大学, 大学院・数理科学研究科, 准教授 (50323465)
MASUDA Tetsu 青山学院大学, 理工学部, 准教授 (00335457)
TSUDA Teruhisa 九州大学, 大学院・数理学研究院, 助教 (00452730)
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| Project Period (FY) |
2007 – 2010
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| Keywords | パンルヴェ系 / 離散可積分系 / 超幾何関数 / τ関数 / 可解カオス系 / 超離散化 |
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| Research Abstract |
Theory of the Painleve systems, which are a certain family of second-order nonlinear integrable differential and difference equations, has been constructed by using the underlying affine Weyl group symmetries and algebraic geometric structures. Based on this framework, detaild studies on solutions have been carried out, such as determination of the sequence of hypergeometric functions arising as solutions. Also, generalizations of the theory of Painleve systems have been developed to higher-order and higher-dimensional systems. Moreover, based on the results obtained above, the theory has been extended to various areas, such as discrete soliton equations, discrete differential geometry, solvable chaotic systems, tropical geometry, complex dynamical systems, and random matrices.
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