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Special solutions and linear monodromy for Painleve equation and Garnier system

Research Project

Project/Area Number 22540237
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionYokkaichi University

Principal Investigator

KANEKO Kazuo  四日市大学, 付置研究所, 研究員 (50571486)

Co-Investigator(Renkei-kenkyūsha) OHYAMA Yousuke  大阪大学, 大学院情報科学研究科, 准教授 (10221839)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords2次元ガルニエ系 / パンルヴェ型方程式 / 有理型解の分類 / 退化系 / モノドロミ / 対称解 / ベックルント変換 / パンルヴェ方程式 / ガルニエ系
Research Abstract

We talked the research results on the transcendental special solutions to the two dimensional degenerate Garnier system and four dimensional Painleve type equations at Math.Society of Japan (Mar.2010, Sept.2010, Mar.2011, Sept.2011, Mar.2012, Sept.2012, Sep. 2013.)
(b) Papers published/submitted. (1) K. Kaneko, Local expansion of Painleve VI transcendents around a fixed singularity, J.Math.Phys. 50 (2009) 013531-1-24. (2) K.Kaneko, Symmetric solutions for the two dimensional degenerate Garnier system G(5), Proc.Japan Acad.Ser.A,Math.Sci., 87 (2011), 114-118. (3) K.Kaneko and Y.Ohyama, Meromorphic Painleve transcendents at a fixed singularity, Math. Nachr. 286 (2013), 861-875. (4) Symmetric solutions to the four dimensional
degenerate Painleve type equation NYA4, J.Nonl.Math.Phys. 21.No. 3 (Sept.2014), 357-370. (5) K.Kaneko, Special solutions and linear monodromy for the two dimensional degenerate Garnier system G(1112), submitted to SIGMA.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (23 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (8 results) (of which Peer Reviewed: 7 results) Presentation (13 results) Remarks (2 results)

  • [Journal Article] Symmetric solutions to the four dimensional degenerate Painleve type equation NY^<A4>2014

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      Journal of Nonlinear Math.Physics

      Volume: Vol.21, No3 Pages: 357-370

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric solutions to the four dimensional degenerate Painlev'e type equation NY^{A4}2014

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      Journal of Nonlinear Mathematical Physics

      Volume: 21 Pages: 357-370

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Special solutions and linear monodromy for the two dimensional degenerate Garnier system G(1112)2013

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      SIGMA

      Volume: arXiv:1310.2006(本論文は2013年10月、雑誌SIGMAに投稿し、現在refereeからの4度目のreport(final)待ち。)

    • Related Report
      2013 Final Research Report
  • [Journal Article] Meromorphic Paileve transcendents at a fixed singularity2013

    • Author(s)
      Kauo Kaneko, Yousuke Ohyama
    • Journal Title

      Math.Nachr.

      Volume: 286, No.8-9 Issue: 8-9 Pages: 861-875

    • DOI

      10.1002/mana.200810241

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Meromorphic Painlev'e transcendents at a fixed singularity2013

    • Author(s)
      Kazuo Kaneko and Yousuke Ohyama
    • Journal Title

      Mathematische Nachrichiten

      Volume: 286 Pages: 861-875

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric solutions for the two dimensional degenerate Garnier system G(5)2011

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      Proc,Japan Acad.

      Volume: 87, Ser.A Pages: 114-118

    • NAID

      40018937032

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric solutionsfor the two dimensional degenerate Gamier system G(5)2011

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      Proceedings of the Japan Academy

      Volume: Vol.87,Ser.A Pages: 114-118

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local expansion of PainLeve VI transcendent around a fixed Singularity2009

    • Author(s)
      Kazuo Kaneko
    • Journal Title

      J.Math.Phys.

      Volume: 50 Pages: 13531-24

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] Symmetric solutions to the degenerate four dimensional Painleve type equations NY^<A4>, IV^<Mat>and II^<Mat>2013

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大
    • Year and Date
      2013-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Symmetric solutions to the degenerate four dimensional Painlev'e type equations NY^{A4}, IV^{Mat} and II^{Mat}2013

    • Author(s)
      金子 和雄
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大 城北キャパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Special solutions to the four dimensional Painleve type equa- tions 21,21,111,111 and 31,22,22,11112012

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      九州大
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 4次元Painleve型方程式21, 21,111,111におけるpoleをもつ特殊解2012

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大
    • Year and Date
      2012-03-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 4次元Painlev'e型方程式21,21,111,111におけるpoleをもつ特殊解2012

    • Author(s)
      金子和雄
    • Organizer
      2012日本数学会年会
    • Place of Presentation
      東京理科大神楽坂キャンパス
    • Year and Date
      2012-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] 4次元Painleve型方程式21, 21,111,111における特殊解と線型モノドロミ2011

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      信州大
    • Year and Date
      2011-09-30
    • Related Report
      2013 Final Research Report
  • [Presentation] 4次元Painlev'e型方程式21,21,111,111における特殊解と線型モノドロミ2011

    • Author(s)
      金子和雄
    • Organizer
      2011日本数学会秋季総合分科会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] 2次元退化Garnie系G(23)における対称解と線型モノドロミ2011

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大
    • Year and Date
      2011-03-23
    • Related Report
      2013 Final Research Report
  • [Presentation] 2次元退化Garnier系G(23)における対称解と線型モノドロミ2011

    • Author(s)
      金子和雄
    • Organizer
      2011日本数学会年会
    • Place of Presentation
      早稲田大西早稲田キャンパス
    • Year and Date
      2011-03-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2次元退化Garnier系G(5), G(14)における対称解と線型モノドロミ2010

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大
    • Year and Date
      2010-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] 2次元退化Garnier系G(5),G(14)における対称解と線型モノドロミ2010

    • Author(s)
      金子和雄
    • Organizer
      2010日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大東山キャンパス
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2次元退化Garnier系における対称解と線型モノドロミ2010

    • Author(s)
      金子和雄
    • Organizer
      日本数学会
    • Place of Presentation
      慶応大
    • Year and Date
      2010-03-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Special solutions to the four dimensional Painlev'e type equations 21,21,111,111 and 31,22,1111

    • Author(s)
      金子 和雄
    • Organizer
      2012日本数学会秋季総合分科会
    • Place of Presentation
      九州大学伊都キャンパス
    • Related Report
      2012 Annual Research Report
  • [Remarks] 関孝和数学研究所が文化講演会を開催(2011-11-20)

    • Related Report
      2011 Annual Research Report
  • [Remarks] 関孝和数学研究所が文化講演会を開催(2010/10/18)

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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