Research on the algebraic structure of theToda type non-autonomous discrete integrable systems and its applications

• Project/Area Number: 18540214
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyoto University
• Principal Investigator: TSUJIMOTO Satoshi Kyoto University, 大学院・情報学研究科, 准教授 (60287977)
• Co-Investigator(Kenkyū-buntansha): NAKAMURA Yoshimasa 京都大学, 大学院・情報学研究科, 教授 (50172458)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,120,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥720,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: アルゴリズム / 応用数学 / 数理工学 / 可積分系

Research Abstract

The analysis on the Toda equation and its related discrete integrable systems has been developed by using the theory of the orthogonal polynomials and the theory of Hirota's tau-function. In particular, we focus on the "non-autonomous discrete integrable systems". Then we are able to construct the theory of these systems from the point of view of the special functions. In addition, we formulate the numerical algorithms of some class of the generalized eigenvalue problems.

Research Products

• [Journal Article] Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy (2010)
  • Author(s): S. Tsujimoto
  • Journal Title: Journal of Systems Science and Complexity Vol.23 Pages: 153-176
  • Peer Reviewed
• [Journal Article] Determinant solutions of the nonautonmous discrete Toda equation associated with the deautonomized discrete KP (2010)
  • Author(s): S.Tsujimoto
  • Journal Title: Journal of Systems Science and Complexity 23 Pages: 153-176
  • Peer Reviewed
• [Journal Article] Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the univ circle (2009)
  • Author(s): S. Tsujimoto, A. Zhedanov
  • Journal Title: SIGMA Vol.5 Pages: 033-30
  • Peer Reviewed
• [Journal Article] Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy (2009)
  • Author(s): S. Tsujimoto and A. Zhedanov
  • Journal Title: Journal of Systems Science and Complexity Vol.5, 033 Pages: 30-30
  • Peer Reviewed
• [Journal Article] Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle (2009)
  • Author(s): S. Tsujimoto, A. Zhedanov
  • Journal Title: Symmetry, Integrability and Geometry : Methods and Applications 5 Pages: 33-30
  • Peer Reviewed
• [Journal Article] Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials (2007)
  • Author(s): V.P. Spiridonov, S. Tsujimoto, A. Zhedanov
  • Journal Title: Communications in Mathematical Physics Vol.272 Pages: 139-165
  • Peer Reviewed
• [Journal Article] Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials (2007)
  • Author(s): V. P. Spiridonov, S. Tsujimoto and A. Zhedanov
  • Journal Title: Communications in Mathematical Physics Vol.272 Pages: 139-165
  • Peer Reviewed
• [Journal Article] Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials (2007)
  • Author(s): V. P. Spiridonov, S. Tsujimoto, A. Zhedanov
  • Journal Title: Communications in Mathematical Physics 272 Pages: 139-165
  • Peer Reviewed
• [Journal Article] A difference analogue of the Davey-Stewartson system: discrete Gram-type determinant solution and Lax pair (2007)
  • Author(s): Gegenhasi, X-B Hu, D. Levi and S. Tsujimoto
  • Journal Title: Journal of Physics A: Mathematical and Theoretical 40 Pages: 12741-12751
  • Peer Reviewed
• [Journal Article] Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy
  • Author(s): S. Tsujimoto
  • Journal Title: Journal of Systems Science and Complexity (To appear)
  • Peer Reviewed
• [Journal Article] Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP
  • Author(s): S. Tsujimoto
  • Journal Title: Journal of Systems Science and Complexity (To appear)
  • Peer Reviewed
• [Journal Article] Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials
  • Author(s): V.P.Spiridonov, S.Tsujimoto, A.Zhedanov
  • Journal Title: Communications in Mathematical Physics (To appear)
• [Presentation] Askey-Wilson積分を用いた歪直交多項式の構成について (2009)
  • Author(s): 三木啓司
  • Organizer: 日本応用数理学会 2009年度年会
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2009-09-29
• [Presentation] 歪直交多項式のスペクトル変形 (2009)
  • Author(s): 三木啓司, 辻本諭
  • Organizer: 日本応用数理学会
  • Place of Presentation: 京都大学
  • Year and Date: 2009-03-08
• [Presentation] On the discrete coupled KP equation (2008)
  • Author(s): S. Tsujimoto
  • Organizer: 7-th AIMS International Conference
  • Place of Presentation: USA
• [Presentation] Discrete KP equation with self-consistent sourcesのグラム型解について (2007)
  • Author(s): 渡邊隆信、辻本諭
  • Organizer: 日本応用数理学会
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-15
• [Presentation] On Hankel determinan formulas of the nonautonomous discrete Toda and Lotka-Volterra equations (2006)
  • Author(s): S. Tsujimoto, Y. Matsui
  • Organizer: SIAM Conference on Nonlinear Waves and Coherence Structures
  • Place of Presentation: USA
• [Presentation] On Hankel determinant formulas of the nonautonomous discrete Toda and Lotka-Volterra equations (2006)
  • Author(s): S. Tsujimoto and Y. Matsui
  • Organizer: SIAM Conference on Nonlinear Waves and Coherent Structures
  • Place of Presentation: USA
• [Remarks] ホームページ