2009 Fiscal Year Final Research Report
Holonomic deformation and nonlinear integrable systems
| Project/Area Number |
18204012
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | The University of Tokyo |
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Principal Investigator |
OKAMOTO Kazuo The University of Tokyo, 大学院・数理科学研究科, 教授 (40011720)
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| Co-Investigator(Kenkyū-buntansha) |
KANIE Yukihiro 三重大学, 教育学部, 教授 (10093121)
SAKAI Hidetaka 東京大学, 大学院・数理科学研究科, 准教授 (50323465)
OHYAMA Yousuke 大阪大学, 大学院・情報科学研究科, 准教授 (10221839)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 可積分系 |
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| Research Abstract |
The aim of present project is to study the theory of holonomic deformation and that of nonlinear integrable systems associated with holonomic deformation. The main subjects of investigation are the Painleve equations and the Garnier systems, which are a generalization in the case of several variables of the Painleve equations. At the beginning of researches of the present project, we have completed studies on Painleve equations by considering the Hamiltonian structure of the two types of the degenerated Painleve equations. The head investigator has published a book, entitled as "Painleve equations", written in Japanese, concerning to the theory of the Painleve equations and the Garnier systems from a viewpoint of holonomic deformation. This contains a historical and mathematical meaning of these integrable systems, and recent development of studies on them. The second aim of the project is to support younger researchers, not only Japanese ones but also foreigners, on theory of integrable systems ; many of them have attended the three international conferences, mainly supported by the project, where they have read their own results.
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