2013 Fiscal Year Final Research Report
Asymptotic analysis of instanton-type solutions
| Project/Area Number |
22540210
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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 |
Basic analysis
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| Research Institution | Kinki University |
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Principal Investigator |
AOKI Takashi 近畿大学, 理工学部, 教授 (80159285)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Takao 近畿大学, 理工学部, 講師 (60527208)
IZUMI Shuzo 近畿大学, 理工学部, 研究員 (80025410)
MATSUI Yutaka 近畿大学, 理工学部, 准教授 (10510026)
NAKAMURA Yayoi 近畿大学, 理工学部, 准教授 (60388494)
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| Co-Investigator(Renkei-kenkyūsha) |
HONDA Naofumi 北海道大学, 大学院理学系研究院, 准教授 (00238817)
KAWAI Takahiro 京都大学, 数理解析研究所, 名誉教授 (20027379)
TAKEI Yoshitsugu 京都大学, 数理解析研究所, 准教授 (00212019)
KOIKE Tatsuya 神戸大学, 大学院理学研究科, 准教授 (80324599)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | インスタントン解 / WKB解 / パンルヴェ階層 / 超幾何微分方程式 / ヴォロス係数 / ストークス現象 / 擬微分作用素 / 核関数 |
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| Research Abstract |
In this research, we have investigated the global properties of solutions to differential equations with a large parameter from the view point of the exact WKB analysis. There are three main results. Firstly, we have constructed the exponential-asymptotic (instanton-type) solutions, namely general formal solutions, to the equations which belong to the first Painleve hierarchies. Secondly, we have classified the topological types of the Stokes curves of the Gauss equation in terms of the parameters of the equation. Thirdly we have defined and computed explicit forms of the Voros coefficients of Gauss equation with a large parameter and obtained the Borel sums go them. We have obtained the formulas that describe parametric Stokes phenomena of WKB solutions.
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