A Generalization of the Painlev'e systems to higher dimension, their special solutions, symmetries and relations to integrables systems

• Project/Area Number: 18740090
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Aoyama Gakuin University (2008); Kobe University (2007); Kyoto University (2006)
• Principal Investigator: MASUDA Tetsu Aoyama Gakuin University, 理工学部, 准教授 (00335457)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,730,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 可積分系 / 特殊函数論 / アフィンワイル群対称性 / 高次元可積分系 / タウ函数 / q^-超幾何函数 / q^-パンルヴェ系 / 反自己双対Yang-Mills 方程式 / 超幾何函数 / q-パンルヴェ系 / 離散パンルヴェ方程式 / 代数解 / 普遍指標多項式 / 点配置空間

Research Abstract

離散パンルヴェ系と呼ばれる非線形力学系の特殊解を具体的に構成し,解として現れる函数がもつ対称性などの性質を,元の力学系の対称性から説明することに成功した.また,ある種の方程式については,解として何故そうした函数が現れるのかについて,ひとつの自然な理由を説明することができた.さらに,離散パンルヴェ系を高次元に拡張することを試み,非常に大きな対称性をもった高次元離散力学系の例を定式化することに成功した.

Research Products

• [Journal Article] Hypergeometric τ-functions of the q-Painlev'e system of type E7(1), Symmetry (2009)
  • Author(s): Tetsu Masuda
  • Journal Title: Integrability and Geometry : Methods and Applications Vol.5
  • Peer Reviewed
• [Journal Article] Hypergeometric τ-functions of the q-Painlev'e system of type E_7^(1) (2009)
  • Author(s): T. Masuda
  • Journal Title: Symmetry, Integrability and Geometry : Methods and Applications 5 Pages: 035-30
  • Peer Reviewed
• [Journal Article] The anti-self-dual Yang-Mills equation and the Painlev'e III equation (2007)
  • Author(s): Tetsu Masuda
  • Journal Title: Journal of Physics A : Mathematical and Theoretical Vol.40, No.48 Pages: 14433-14445
  • Peer Reviewed
• [Journal Article] The anti-self-dual Yang-Mills equation and the Painleve III equation (2007)
  • Author(s): T. Masuda
  • Journal Title: Journal of Physucs A 40 Pages: 14433-14445
  • Peer Reviewed
• [Journal Article] Point configurations, Cremona transformations and the elliptic difference Painlev'e equation (2006)
  • Author(s): Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and Yasuhiko Yamada
  • Journal Title: S'eminaires et Congr`es Vol.14 Pages: 175-204
  • Peer Reviewed
• [Journal Article] q-Painlev'e VI equation arising from q-UC hierarchy (2006)
  • Author(s): Teruhisa Tsuda and Tetsu Masuda
  • Journal Title: Communications in Mathematical Physics Vol.262, No.3 Pages: 595-609
  • Peer Reviewed
• [Journal Article] q-Painleve VI equation arising from q-UC hierarchy (2006)
  • Author(s): T.Tsuda
  • Journal Title: Communications in Mathematical Physics 262 Pages: 595-609
• [Journal Article] Point configurations, Cremona transformations and the elliptic difference Painleve equation (2006)
  • Author(s): K.Kajiwara
  • Journal Title: Seminaires et Congres 14 Pages: 175-204
• [Presentation] q-Painlev'e系の超幾何タウ函数 (2008)
  • Author(s): 増田哲
  • Organizer: 日本数学会・無限可積分系セッション
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] E8(1)型q-Painlev'e系の超幾何タウ函数 (2007)
  • Author(s): 増田哲
  • Organizer: 研究集会「ソリトンの数理とその応用:非線形波動から可積分系へ」
  • Place of Presentation: 湯田簡易保険保養センター
  • Year and Date: 2007-12-23
• [Presentation] E_8^<(1)>型 q-Painleve 系の超幾何タウ函数 (2007)
  • Author(s): 増田 哲
  • Organizer: 研究集会「ソリトンの数理とその応用:非線形波動から可積分系へ」
  • Place of Presentation: 湯田簡易保険保養センター
  • Year and Date: 2007-12-23
• [Presentation] E8(1)型q-Painlev'e系の超幾何タウ函数 (2007)
  • Author(s): 増田哲
  • Organizer: 研究集会「非線形波動研究の歩みと展望」
  • Place of Presentation: 九州大学応用力学研究所
  • Year and Date: 2007-11-07
• [Presentation] E_8^<(1)>型 q-Painleve 系の超幾何タウ函数 (2007)
  • Author(s): 増田 哲
  • Organizer: 研究集会「非線形波動研究の歩みと展望」
  • Place of Presentation: 九州大学応用力学研究所
  • Year and Date: 2007-11-07
• [Presentation] パンルヴェ系の代数解に付随する特殊多項式 (2007)
  • Author(s): 増田哲
  • Organizer: 応用数理学会・応用可積分系研究部会オーガナイズドセッション
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-15
• [Presentation] パンフヴェ系の代数解に付随する特殊多項式 (2007)
  • Author(s): 増田 哲
  • Organizer: 応用数理学会・応用可積分系研究部会
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-15
• [Presentation] Painlev'e V方程式の超幾何解と反自己双対Yang-Mills方程式 (2007)
  • Author(s): 増田哲
  • Organizer: 研究集会「可積分系数理の新潮流」
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2007-08-21
• [Presentation] Painleve V 方程式の超幾何解と反自己双対 Yang-Mills 方程式 (2007)
  • Author(s): 増田 哲
  • Organizer: 研究集会「可積分系数理の新潮流」
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2007-08-21
• [Presentation] 反自己双対 Yang-Mills 方程式と Painleve V 方程式 (2007)
  • Author(s): 増田 哲
  • Organizer: 函数方程式論サマーセミナー
  • Place of Presentation: ビレッジ安曇野
  • Year and Date: 2007-08-06
• [Presentation] パンルヴェ方程式および離散パンルヴエ方程式の特殊解 (2007)
  • Author(s): 増田 哲
  • Organizer: 青山学院大学理工学部物理・数理科学コロキウム
  • Place of Presentation: 青山学院大学
  • Year and Date: 2007-07-13
• [Presentation] Tau functions of the hypergeometric solutions to the q-difference Painlev'e system of type E7(1) (2006)
  • Author(s): Tetsu Masuda
  • Organizer: The 7th International Conference on Symmetries and Integrability of Difference Equations
  • Place of Presentation: The University of Melbourne, Melbourne
  • Year and Date: 2006-07-13
• [Presentation] The anti-self-dual Yang-Mills equation and the third Painlev'e equation, Algebraic (2006)
  • Author(s): Tetsu Masuda
  • Organizer: Analytic and Geometric Aspects of Complex Differential Equations and their Deformations. Painlev'e Hierarchies
  • Place of Presentation: RIMS, Kyoto University
  • Year and Date: 2006-05-19
• [Presentation] Ernst方程式,Painlev'e方程式,特殊函数 (2006)
  • Author(s): 増田哲
  • Organizer: 研究集会「ソリトン・特殊関数・変換理論」
  • Place of Presentation: 国民宿舎つづらお荘
  • Year and Date: 2006-05-13