Study of integrable systems coming from field theories and theirapplications

• Project/Area Number: 18540210
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ochanomizu University
• Principal Investigator: TAKEBE Takash Ochanomizu University, 大学院・人間文化創成科学研究科, 准教授 (60240727)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,060,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥660,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 可積分系 / 無分散系 / 簡約 / Loewner方程式 / SLE / アフィン・リー代数 / affine Lie代数 / 特異ベクトル / 無分散可積分系 / universal Whitham hierarchy / 国際研究者交流 / アメリカ:イタリア

Research Abstract

無分散型と呼ばれる可積分な偏微分方程式系の解の構成方法として、本質的な独立変数の個数を制限する「簡約」という操作について、種々の無分散系(特に多成分系)を対象に研究した。また、統計力学や確率論の方面からも注目されいているStochastic Loewner Evolution(SLE)を、高い対称性(アフィン・リー代数の対称性)を持つ場合に拡張する事を試みた。

Research Products

• [Journal Article] Loewner equations, Hirota equations and reductions of universal Whitham hierarchy (2008)
  • Author(s): K. Takasaki and T. Takebe
  • Journal Title: Journal of Physics A 41 Pages: 475206-27
  • Peer Reviewed
• [Journal Article] Loewner equations, Hirota equations and reductions of universal Whitham hierarchy (2008)
  • Author(s): K. Takasaki. T, Takebe
  • Journal Title: Journal of Physics A 41 Pages: 1-27
  • Peer Reviewed
• [Journal Article] Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy (2007)
  • Author(s): K. Takasaki and T. Takebe
  • Journal Title: Physica D235 Pages: 109-125
  • Peer Reviewed
• [Journal Article] Universal Whitham hierarechy, dispersionless Hirota equations and component KP hierarchy (2007)
  • Author(s): K. Takasaki and T. Takebe
  • Journal Title: Physica D 235 Pages: 109-125
  • Peer Reviewed
• [Journal Article] Loewner equations and dispersionless hierarchies (2006)
  • Author(s): T. Takebe, L. -P. Teo and A. Zabrodin
  • Journal Title: Journal of Physics A 39 Pages: 11479-11501
  • Peer Reviewed
• [Journal Article] Coupled modified KP hierarchy and its dispersionless limit, Symmetry (2006)
  • Author(s): T. Takebe and L.-P. Teo
  • Journal Title: Integrability and Geometry : Methods and Applications(電子シャーナル) 2 Pages: 072-30
  • Peer Reviewed
• [Journal Article] Lowner equations and dispersionless hierarchies (2006)
  • Author(s): T.Takebe, L.-P.Teo, A.Zabrodin
  • Journal Title: Journal of Physics A 39 Pages: 11479-11501
• [Journal Article] Coupled modified KP hierarchy and its dispersionless limit (2006)
  • Author(s): T.Takebe, L.-P.Teo
  • Journal Title: Symmetry, Integrability and Geometry : Methods and Applications 2 Pages: 72-72
• [Presentation] Laplacian Growth and Related Topics (2008)
  • Author(s): Takashi Takebe
  • Organizer: Dispersionless Hirota Equations and Reduction of Integrable Hierarchies, Workshop
  • Place of Presentation: Centre de Recherche Mathematiques, Montreal(Canada)
  • Year and Date: 2008-08-21
• [Presentation] Dispersionless Hirota Equations and Reduction of Integrable Hierarchies (2008)
  • Author(s): 武部 尚志
  • Organizer: Laplacian Growth and Related Topics
  • Place of Presentation: Centre de Recherche Mathematiques (モントリオール、カナダ)
  • Year and Date: 2008-08-21
• [Presentation] Loewner equations and dispersionless hierarchies (2006)
  • Author(s): Takashi Takebe
  • Organizer: Conference on Integrable Systems in Applied Mathematics
  • Place of Presentation: Colmenarejo Campus of the Carlos III University(Madrid, Spain)
  • Year and Date: 2006-09-11
• [Presentation] 無分散可積分系と関数論 (2006)
  • Author(s): 武部尚志
  • Organizer: 研究会「可積分系数理の眺望」
  • Place of Presentation: 京都大学・数理解析研究所
  • Year and Date: 2006-08-23
• [Book] 可解格子模型と共形場理論の話題から (2006)
  • Author(s): 武部尚志, 関谷信寛
  • Total Pages: 120
  • Publisher: 上智大学理工学部数学科