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Studies on the Painleve equations

Research Project

Project/Area Number 08454005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

UMEMURA Hiroshi  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (40022678)

Co-Investigator(Kenkyū-buntansha) MUKAI Shigeru  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (80115641)
NAMIKAWA Yukihiko  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (20022676)
KITOKA Yosiyuki  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (40022686)
TSUCHIYA Akohiro  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (90022673)
AOMOTO Kazuhiko  Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (00011495)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥4,800,000 (Direct Cost: ¥4,800,000)
Fiscal Year 1997: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1996: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsPainleve equations / Special polynomials / Baecklund transformations / Painlev'e equations / BaeckLund変換 / Painleve方程式 / 特殊関数 / モノドロミ-保変形
Research Abstract

(1) We succeeded in generating special polynomials by Painleve equations, which generalize the Yablonskii-Vorob'ev polynomial for the second Painleve equation and the Okamoto polynomial for the fourth Painleve equation, Polynomials of particular interest appeared in algebraic solutions of the third, the fifth, and the sixth equations.
(2) As for the polynomials associated with algebraic solutions of the sixth equation, we formulated a conjecture that each coefficient of the polynomials is equal to the degree of the representation of GL given by an explicit Young diagram.
(3) The above conjecture was recently settled.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] H.UMEMURA: "Galoir theory of algebrain and differential equaters" Nagoya Math.J.144. 1-58 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Differential Galuig theory of infinite dimension" Nagoya Math.J.144. 59-135 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Lie-Drach-Vesiof Theory" Adv.Shudies in Pure Math.25. 364-358 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Solutions of the second and fouilh Painleve equations" Nagoya Math.J.148. 151-198 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Special polynomials asociated noth the Painleve equations" Proc.Workshop on the special functions. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Iireducifility of the Painleve equations" Proc.Workshop on the special functions. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Galois theory of algebraic and differential Equations" Nagoya Math.J.144. 1-58 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Differential Galois theory of infinte Dimension" Nagoya Math.J.144. 59-135 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Lie-Drach-Vessiot theory" Adv.Studies in Pure Math.25. 346-358 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Solutions of the second and fourth Painleve equations" Nagoya Math.J.148. 151-198 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Special polynomials associated with the Painleve equations, to appear" Proc.Workshop on Special functions, Montreal. (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Umemura: "Irreducibility of the Painleve equations to appear" Proc.Workshop on Special functions, Montreal. (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.UMEMURA: "Galces thiory of algebrai and differential equations" Nagoya Math. J.144. 1-58 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.UMEMURA: "Differential Gahis theory of infinite dimension" Nagoya Math. J.144. 59-135 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.UMEMURA: "Lie-Drach-Verinot Thecry" Adv.Stridies in Pure Math.25. 311-358 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.UMEMURA: "Solutions of the second and fourth Painlev'e equations" Nagoya Math. J.144. 151-198 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.UMEMURA: "Special polynomials associated with the Painlev'e equations" hoc.Workshop on the special functions,. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.UMEMURA: "Irreducilility of the Painlev'e equations" hoc.Workshop on the special functions,. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 梅村 浩: "Galois Theory of algebraic and diflerential equations" Nagoya Math.J.144. 1-58 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 梅村 浩: "Differential Galos theory of infinite dimension" Nagoya Math.J.144. 59-135 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 梅村 浩(渡辺文彦): "Solutions of the second and fourth Painleve equatiens" Nagoya Math.J.(1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 梅村 浩: "Irreducilility of the Painleve equatiens" Roc.of Workshop on the Thecry of Nonlinear Special functions Montreal,. (発売予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] 梅村 浩: "Special polymomials assaciated with the Painlove equatiens" Roc.of Workshop on the Thecry of Nonlinear Special functions Montreal,. (発売予定).

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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