| Project/Area Number |
20340028
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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 |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
KAWAI Takahiro 京都大学, 数理解析研究所, 名誉教授 (20027379)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEI Yoshitsugu 京都大学, 数理解析研究所, 准教授 (00212019)
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Tatsuya 神戸大学, 理学(系)研究科(研究院), 准教授 (80324599)
AOKI Takashi 近畿大学, 理工学部, 教授 (80159285)
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| Research Collaborator |
KAMIMOTO Shingo 東京大学, 数理科学研究科, 院生
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Fiscal Year 2011: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2010: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2008: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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| Keywords | 高階パンルヴェ方程式 / インスタントン型解 / 単純極作用素 / fixed singularities / 完全 WKB 解析 / 超局所解析 / 解析的 S-行列 / 3 粒子閾値 / M2P1Tシュレーディンガー方程式 / 完全WKB解析 / 解析的S-行列 / trussbridge diagram函数 / 変わり点 / 超局所解析学 / Toulouse Project / Mathieu方程式 / Voros係数 / 仮想的変わり点 / MPPT作用素 / alien calculus / ゴースト作用素 / 2重変わり点作用素 / ガルニエ系 / MTP作用素 |
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| Research Abstract |
1. Near a turning point of type 1 of a higher order Painleve equation (P_J)_m(J=I, II, IV; m = 1, 2, …) each instanton-type solution of (P_J)_m is transformed to a solution of the second order Painleve equation (P_I)_1. The proof makes essential use of the semi-global WKB theoretic transformation of the Schrodinger equation that underlies (P_J)_m.
2. We have studied a class of Schrodinger equation whose WKB-theoretic canonical form is an algebraic Mathieu equation, and the analytic structure of WKB solutions of such equations is clarified by microlocal analysis.
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