The theory of structure of higher order Painleve equations that is based on the exact WKB analysis

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20340028
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: KAWAI Takahiro Kyoto University, 数理解析研究所, 名誉教授 (20027379)
• Project Period (FY): 2008 – 2011
• Keywords: 高階パンルヴェ方程式 / 完全WKB解析 / 変わり点 / 単純極作用素 / 超局所解析学

Research Abstract

(1) 手段としての完全WKB解析を理論的に進展させることにより、
(2) 対象である高階パンルヴェ方程式の構造の理解を深める。
その過程において
(3) 完全WKB解析と超局所解析学の交錯点を具体的に探る。

Research Products

• [Journal Article] On the Voros coefficients for the Whittaker equation with a large parameter (2011)
  • Author(s): T.Koike, Y.Takei
  • Journal Title: Publ.RIMS 47(in press.)
• [Journal Article] WKB analysis of higher order Painleve equations with a large parameter. II. (2011)
  • Author(s): T.Kawai, Y.Takei
  • Journal Title: Publ.RIMS 47 Pages: 153-219
  • Peer Reviewed
• [Journal Article] On the WKB theoretic structure of a Schrodinger operator with a merging pair of a simple pole and a simple turning point (2010)
  • Author(s): S.Kamimoto, T.Kawai, T.Koike, Y.Takei
  • Journal Title: Kyoto J.Math. 50 Pages: 101-164
  • Peer Reviewed
• [Journal Article] The Bender-Wu analysis and the Voros theory. II. (2009)
  • Author(s): T.Aoki, T.Kawai, Y.Takei
  • Journal Title: Advanced Studies in Pure Mathematics, Math.Soc.Japan 54 Pages: 19-94
  • Peer Reviewed
• [Journal Article] Sato's conjecture for the Weber equation and transformation theory for Schrodinger equations with a merging pair of turning points (2008)
  • Author(s): Y.Takei
  • Journal Title: RIMS Kokyuroku Bessatsu, B 10 Pages: 205-224
  • Peer Reviewed
• [Presentation] An overview on the resurgent analysis of one-dimensional Schrodinger equations (2010)
  • Author(s): Y.Takei
  • Organizer: RIMS共同研究「Exact WKB analysis-Borel summability of WKB solutions」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-09-08
• [Presentation] 1次元Schrodinger方程式の完全WKB解析---WKB解のBorel変換の特異点について--- (2010)
  • Author(s): Y.Takei
  • Organizer: RIMS研究集会「可積分系数理の多様性」
  • Place of Presentation: 京都大学数理解析研究所<招待講演>
  • Year and Date: 2010-08-19
• [Presentation] On the turning point problem for instanton-type solutions of (higher order) Painleve equations (2009)
  • Author(s): Y.Takei
  • Organizer: Asymptotics in dynamics, geometry and PDEs ; generalized Borel summation
  • Place of Presentation: E.De Giorgi数学研究センター(イタリア)<招待講演>
  • Year and Date: 2009-10-16
• [Presentation] On a Schrodinger equation with a merging pair of a simple pole and a simple turning point---Alien calculus of WKB solutions through microlocal analysis (2009)
  • Author(s): S.Kamimoto, T.Kawai, T.Koike, Y.Takei
  • Organizer: International Conference "Asymptotics in dynamics, geometry and PDEs ; generalized Borel summation"
  • Place of Presentation: E.De Giorgi数学研究センター(イタリア)<招待講演>
  • Year and Date: 2009-10-15
• [Presentation] Transformation theory for MTP equations and singularity structure of the Borel transform of their WKB solutions (2008)
  • Author(s): Y.Takei
  • Organizer: RIMS合宿型セミナー「Foundations of exact WKB analysis and resurgence theory」
  • Place of Presentation: 関西セミナーハウス
  • Year and Date: 20081217-20081218
• [Book] 特異摂動の代数解析学 (2008)
  • Author(s): 河合隆裕・竹井義次
  • Total Pages: 146
  • Publisher: 岩波書店
• [Remarks] 河合がSpringer社より近日刊行予定の啓蒙書「数理物理;私の研究」に寄稿。