2012 Fiscal Year Final Research Report
Geometric methods in discrete integrablesystems
| Project/Area Number |
21340036
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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 | Kobe University |
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Principal Investigator |
YAMADA Yasuhiko 神戸大学, 大学院・理学研究科, 教授 (00202383)
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| Co-Investigator(Kenkyū-buntansha) |
NOUMI Masatohi 神戸大学, 自然科学系先端融合研究環重点研究部, 教授 (80164672)
OHTA Yasuhiro 神戸大学, 大学院・理学研究科, 教授 (10213745)
SAITO Masahiko 神戸大学, 大学院・理学研究科, 教授 (80183044)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 離散可積分系 / ラックス表示 / 幾何学 / 特殊解 / パデ近似 / 共形場理論 |
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| Research Abstract |
We studied mainly the discrete Painleve equations. The Lax formalism for various cases including the elliptic difference Painleve equation of type E_8 was constructed, and its geometric characterization was clarified. We constructed the corresponding Pade interpolation problem and derive simple expressions for the Painleve equation, Lax form and special solutions. Relations among the Gauge theory, conformal field theory and quantum Painleve equations were also studied.
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