Special solutions and linear monodromy for Painleve equation and Garnier system

2013 Fiscal Year Final Research Report

• Project/Area Number: 22540237
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Yokkaichi 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
• Keywords: 2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

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.

Research Products

• [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
  • 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。)
• [Journal Article] Meromorphic Paileve transcendents at a fixed singularity (2013)
  • Author(s): Kauo Kaneko, Yousuke Ohyama
  • Journal Title: Math.Nachr. Volume: 286, No.8-9 Pages: 861-875
  • DOI: 10.1002/mana.200810241
  • 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
  • Peer Reviewed
• [Journal Article] Local expansion of PainLeve VI transcendent around a fixed Singularity (2009)
  • Author(s): Kazuo Kaneko
  • Journal Title: J.Math.Phys. Volume: 50 Pages: 013531-24
  • 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
• [Presentation] Special solutions to the four dimensional Painleve type equa- tions 21,21,111,111 and 31,22,22,1111 (2012)
  • Author(s): 金子和雄
  • Organizer: 日本数学会
  • Place of Presentation: 九州大
  • Year and Date: 2012-09-18
• [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
• [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
• [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
• [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
• [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