2017 Fiscal Year Final Research Report
The exact WKB analysis for Painleve hierarchies
| Project/Area Number |
15K17557
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
Umeta Yoko 山口大学, 大学院創成科学研究科, 助教 (90606386)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 完全WKB解析 / 漸近解析 / 非線型方程式 / パンルヴェ階層 / インスタントン解 / ストークス幾何 / Lax pair / ストークス現象 |
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| Outline of Final Research Achievements |
We study higher order Painleve equations from a view point of the exact WKB analysis.Instanton-type solutions are constructed for P_J-hierarchies(J=I,II,IV,
34).To study the common structures between the P_J-hierarchies,a unified family of P_J-hieararchies(J=I,II,IV,34)is introduced.By using the system,we study a construction of instanton-type solutions for Painleve hierarchies. We also proved that the Stokes geometry of the system has the following intrinsic relationship with its underlying Lax pair:If t (t is the variable of unknown functions)lies on a Stokes curve of non-linear ordinary differential equations, some degenerate phenomenon occurs in the Stokes geometry of the underlying Lax pair.
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| Free Research Field |
数学, 基礎解析学
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