| Project/Area Number |
19540207
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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 |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
HASEGAWA Koji Tohoku University, 大学院・理学研究科, 講師 (30208483)
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| Co-Investigator(Kenkyū-buntansha) |
黒木 玄 東北大学, 大学院・理学研究科, 助教 (10234593)
菊地 哲也 東京大学, 大学院・数理科学研究科, 研究拠点形成特任研究員 (00374900)
名古屋 創 慶応義塾大学, 大学院・理工学研究科, 特別研究助教(非常勤) (80447367)
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| Co-Investigator(Renkei-kenkyūsha) |
KUROKI Gen 東北大学, 大学院・理学研究科, 助教 (10234593)
KIKUCHI Tetsuya 東京大学, 大学院・数理科学研究科, 特任研究員 (00374900)
NAGOYA Hajime 東京大学, 大学院・数理科学研究科, 特任研究員 (80447367)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | パンルヴェ方程式 / ソリトン系 / 対称性 / 量子群 / 量子化 / 差分化 / 可積分系 / パンルベ方程式 / ソリトン / モノドロミー保存変形 / 非線形 / 離散化 / ランダム行列 |
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| Research Abstract |
Panleve equations are second order nonlinear ordinary differential equations with certain good properties discovered in early 1900s. They are nonautonomous Hamiltonian systems allowing affine Weyl group symmetry, arise from monodromy preserving equations as well as solitonic partial differential equations through dimensional reduction. Painleve type equations are those equations with high symmetry, partial or of higher order in general, arising in similar ways. We investigate the canonical quantization of Painleve type equations and difference versions thereof. In particular we gave the quantized difference Painleve equations via the reduction of quantized solitonic systems, as well as the formulation as generalization of conformal field theories.
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