Study of methods for analysing continuous systems, relying ondiscrete and ultra-discrete systems

• Project/Area Number: 18540204
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: WILLOX Ralph The University of Tokyo, 大学院・数理科学研究科, 准教授 (20361610)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,090,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥690,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 可積分系 / 超離散極限 / セルオートマトン / 離散系

Research Abstract

連続の力学系に対して新しい離散化手法を考案し、その手法の結果で得られた離散系とセルオートマトンの性質をもとの連続系の振る舞いと関連づけることに成功した。特に、提案した離散化手法の妥当性を計るため、様々な自然現象を記述する連続模型の離散化を行ない、それぞれの模型に対応する離散系から、「超離散化」と呼ばれているテクニックによって適切なセルオートマトンを系統的に構成し、これらのセルオートマトンの示す挙動がもとの自然現象に類似しているものであることを示した。

Research Products

• [Journal Article] On two (not so) new integrablepartial difference equations (2009)
  • Author(s): A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
  • Journal Title: Journal ofPhysics A : Mathematical and Theoretical 掲載決定済み
  • Peer Reviewed
• [Journal Article] Yang-Baxter maps and the discrete Kphierarchy (2009)
  • Author(s): S. Kakei, J.J.C. Nimmo, R. Willox
  • Journal Title: Glasgow Mathematical Journal 51A Pages: 107-119
  • Peer Reviewed
• [Journal Article] Yang-Baxter maps and the discrete KP hierarchy (2009)
  • Author(s): S. Kakei et al.
  • Journal Title: Glasgow Mathematical Journal 51A Pages: 107-119
  • Peer Reviewed
• [Journal Article] Contiguity relations for discrete andultradiscrete Painleve equation (2008)
  • Author(s): A. Ramani, B. Grammaticos, R. Willox
  • Journal Title: Journalof Nonlinear Mathematical Physics 15 Pages: 353-364
  • Peer Reviewed
• [Journal Article] Bilinearisation and solutions of the KdV6equation (2008)
  • Author(s): A. Ramani, B. Grammaticos, R. Willox
  • Journal Title: Analysis and Applications 6 Pages: 401-412
  • Peer Reviewed
• [Journal Article] Discretisation-induced delaysand their role in the dynamics (2008)
  • Author(s): A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
  • Journal Title: Journal ofPhysics A : Mathematical and Theoretical 41
  • Peer Reviewed
• [Journal Article] Discretisation-induced delays and their role in the dynamics (2008)
  • Author(s): A. Ramani et al.
  • Journal Title: J. Phys. A: Mathematical and Theoretical 41
  • Peer Reviewed
• [Journal Article] Bilinearisation and solutions of the KdV6 equation (2008)
  • Author(s): A. Ramani et al.
  • Journal Title: Analysis and Applications 6 Pages: 401-412
  • Peer Reviewed
• [Journal Article] Contiguity relations for discrete and ultradiscrete Painleve equations (2008)
  • Author(s): A. Ramani et al.
  • Journal Title: Journal of Nonlinear Mathematical Physics 15 Pages: 353-364
  • Peer Reviewed
• [Journal Article] Discretization-induced delays and their role in the dynamics (2008)
  • Author(s): A. Ramani, et. al.
  • Journal Title: Journal of Physics A: Mathematical and Theoretical 41(投稿中(掲載確定))
  • Peer Reviewed
• [Journal Article] Constructinglump-like solutions of the Hirota-Miwaequation (2007)
  • Author(s): B. Grammaticos, A. Ramani, V. Papageorgiou, J. Satsuma, R. Willox
  • Journal Title: Journal of Physics A : Mathe-matical and Theoretical 40 Pages: 12619-12627
  • Peer Reviewed
• [Journal Article] From limit cycles to periodicorbits through ultradiscretisation (2007)
  • Author(s): R. Willox, A. Ramani, J. Satsuma, B.Grammaticos
  • Journal Title: Physica A 385 Pages: 473-486
  • Peer Reviewed
• [Journal Article] From limit cycles to periodic orbits through ultradiscretisation (2007)
  • Author(s): R. Willox, et. al.
  • Journal Title: Physica A 385 Pages: 473-486
  • Peer Reviewed
• [Journal Article] Constructing lump-like solutions of the Hirota-Miwa equation (2007)
  • Author(s): B. Grammaticos, et. al.
  • Journal Title: Journal of Physics A: Mathematical and Theoretical 40 Pages: 12619-12627
  • Peer Reviewed
• [Presentation] Crystal-like structuresarising from the dKP hierarchy (2009)
  • Author(s): R. Willox
  • Organizer: Geometric Aspects of Discrete andUltra-Discrete Integrable Systems
  • Place of Presentation: University ofGlasgow、 スコットランド(連合王国)
  • Year and Date: 2009-03-30
• [Presentation] Construction of Yang-Baxter maps from the discrete Kphierar- chy (2008)
  • Author(s): R. Willox
  • Organizer: Aspects of QuantumIntegrability
  • Place of Presentation: 京都大学基礎物理学研究所
  • Year and Date: 2008-07-24
• [Presentation] Construction of Yang-Baxter maps from the discrete KP hierarchy (2008)
  • Author(s): R. Willox
  • Organizer: Aspects of Quantum Integrability
  • Place of Presentation: 京都大学
  • Year and Date: 2008-07-24
• [Presentation] "Box and Ball"systems and Yang-Baxter maps (2008)
  • Author(s): R. Willox, Discrete KP
  • Organizer: Nonlinear Waves - Theory and Applications
  • Place of Presentation: 北京(中国)
  • Year and Date: 2008-06-09
• [Presentation] Discrete KP, "Box and Ball" systems and Yang-Baxter maps (2008)
  • Author(s): R. Willox
  • Organizer: Nonlinear Waves-Theory and Applications
  • Place of Presentation: 北京(中国)
  • Year and Date: 2008-06-09
• [Presentation] Local Darboux transformationsand geometric crystals (2007)
  • Author(s): R. Willox
  • Organizer: Alge-braic aspects of integrable systems
  • Place of Presentation: Islay、スコットランド(連合王国)
  • Year and Date: 2007-07-02