Construction of special solutions to Painleve systems and the quest for infinite-dimensional integrable systems
| Project/Area Number |
21740126
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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 | Aoyama Gakuin University |
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Principal Investigator |
MASUDA Tetsu 青山学院大学, 理工学部, 准教授 (00335457)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 可積分系 / 離散羃函数 / 笹野系 / q-類似 / タウ函数 / 数理物理 / 離散冪函数 / 第6パンルヴェ方程式 / アフィンワイル群対称性 / 高次元可積分系 / q-超幾何函数 / q-パンルヴェ系 |
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| Research Abstract |
We constructed several special solutions to the discrete Painleve systems. We determined the tau-functions of the solutions completely, and gave a natural description for some properties of the functions that appear as the solutions from the viewpoint of the affine Weyl group symmetry. We also constructed an explicit formula for the discrete power function in terms of the hypergeometric type solutions to the sixth Painlve equation. Moreover, we tried to construct a discrete analogue and special solutions of the higer-order Painleve systems to pave the way for discovering new infinite dimensional integrable systems
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Report
(5 results)
Research Products
(46 results)
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[Presentation] 離散羃函数の明示公式2010
Author(s)
増田哲
Organizer
非線形波動研究の新たな展開-現象とモデル化-
Place of Presentation
九州大学応用力学研究所
Year and Date
2010-10-29
Related Report
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