2012 Fiscal Year Final Research Report
Geometric study of Painleve equations and infinite integrable systems
| Project/Area Number |
21740123
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Hitotsubashi University (2011-2012)
Kyushu University (2009-2010) |
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Principal Investigator |
TSUDA Teruhisa 一橋大学, 大学院・経済学研究科, 准教授 (00452730)
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| Project Period (FY) |
2009 – 2012
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| Keywords | パンルヴェ方程式 / 可積分系 / 超幾何函数 |
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| Research Abstract |
The UC hierarchy is an extension of the KP hierarchy, which is an infinite-dimensional integrable system associated with the universal rational character of the general linear group. Through a similarity reduction we derive from the UC hierarchy a class of the Schlesinger systems including the Garnier system and the sixth Painleve equation, which describes the monodromy preserving deformations of Fuchsian linear differential equations with certain spectral types. We also present a unified formulation of the above Schlesinger systems as a polynomial Hamiltonian system and their particular solutions in terms of a certain generalization of Gauss' hypergeometric function.
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