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Detecting integrability of discrete equations on multi-dimensional lattices

Research Project

Project/Area Number 16H06711
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

Mase Takafumi  東京大学, 大学院数理科学研究科, 特任助教 (80780105)

Project Period (FY) 2016-08-26 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords可積分系 / 離散可積分系 / 代数的エントロピー / 応用数学 / 特異点閉じ込め / 可積分性判定
Outline of Final Research Achievements

We studied the integrability of discrete equations on multi-dimensional lattices, by means of cancellation of factors. First, we extended the so-called coprimeness condition. As a result, it has become possible to apply the coprimeness condition to more equations than before. We also showed that the nonlinear form of an extended version of the discrete Toda equation possesses this property. Moreover, in the case of equations on one-dimensional lattices, we developed a method to verify the integrability only by means of singularity confinement. Using the theory of algebraic surfaces, we revealed the meaning of our method in the case of second-order mappings.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • Research Products

    (10 results)

All 2018 2017 2016

All Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (5 results) (of which Int'l Joint Research: 2 results)

  • [Journal Article] A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence2018

    • Author(s)
      Ryo Kamiya, Masataka Kanki, Takafumi Mase, and Tetsuji Tokihiro
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 51 Issue: 12 Pages: 125203-125203

    • DOI

      10.1088/1751-8121/aaad47

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Calculating algebraic entropies: an express method2017

    • Author(s)
      A. Ramani, B. Grammaticos, R. Willox and T. Mase
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 50 Issue: 18 Pages: 185203-185203

    • DOI

      10.1088/1751-8121/aa66d7

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation2017

    • Author(s)
      Ryo Kamiya, Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
    • Journal Title

      Journal of Mathematical Physics

      Volume: 58 Issue: 1 Pages: 012702-012702

    • DOI

      10.1063/1.4973744

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Full-deautonomisation of a lattice equation2016

    • Author(s)
      R. Willox, T. Mase, A. Ramani and B. Grammaticos
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 49 Issue: 28 Pages: 28LT01-28LT01

    • DOI

      10.1088/1751-8113/49/28/28lt01

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Singularity confinement and chaos in two-dimensional discrete systems2016

    • Author(s)
      Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 49 Issue: 23 Pages: 23LT01-23LT01

    • DOI

      10.1088/1751-8113/49/23/23lt01

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 特異点閉じ込めと代数的エントロピー I2017

    • Author(s)
      間瀬崇史, R. Willox, A. Ramani, B. Grammaticos
    • Organizer
      非線形波動研究の新潮流 -理論とその応用-
    • Related Report
      2017 Annual Research Report
  • [Presentation] Spaces of initial conditions for nonautonomous mappings of the plane2017

    • Author(s)
      T. Mase
    • Organizer
      The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
    • Place of Presentation
      Athens (アメリカ、ジョージア州)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非自励2階差分方程式の初期値空間2017

    • Author(s)
      間瀬崇史
    • Organizer
      アクセサリー・パラメーター研究会2017
    • Place of Presentation
      熊本大学理学部 (熊本県熊本市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Spaces of initial conditions for nonautonomous mappings of the plane2016

    • Author(s)
      T. Mase
    • Organizer
      Workshop on Discrete Painleve equations
    • Place of Presentation
      東京大学数理科学研究科 (東京都目黒区)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 多次元格子上の擬似可積分系2016

    • Author(s)
      間瀬崇史
    • Organizer
      可積分系数理の現状と展望
    • Place of Presentation
      京都大学数理解析研究所 (京都府京都市)
    • Related Report
      2016 Annual Research Report

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Published: 2016-09-02   Modified: 2019-03-29  

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