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Studies on integrable cellular automata

Research Project

Project/Area Number 23740126
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionNihon University

Principal Investigator

MADA Jun  日本大学, 生産工学部, 助教 (80396853)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords可積分系 / セルオートマトン / 有限体 / 相関関数 / 箱玉系 / 超離散化 / 超離散 / 量子化
Research Abstract

I investigated (1) discrete integrable equations over finite fields and (2) a classification of an elementary cellular automaton.
(1) (i) Replacing a parameter with a value in finite fields, one can uniquely determine the values of the dependent variables in finite fields and infinity. Thanks to this property, I obtained the time evolution and N soliton solutions of the (generalized) discrete KdV equations over finite fields. (ii) I defined the notion of almost good reduction (AGR), which is an arithmetic analogue of passing the singularity confinement test, and proved that the discrete Painleve II equation (dPII) has AGR. By AGR, I obtained the time evolution and a solution of the dPII over finite fields. I had the similar results for qPII, qPIII, qPIV and dKdV.
(2) I suggested a classification of an elementary cellular automaton by singular value decomposition. Though class 4 resembles class 3 of Wolfram's classification, one can distinguish them by using the above method.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (20 results)

All 2014 2013 2012 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (12 results)

  • [Journal Article] Singularities of the discrete KdV equation and the Laurent property2014

    • Author(s)
      KANKI, Masataka
    • Journal Title

      Journal of Physics A : Mathematical and Theoretical

      Volume: 47 Issue: 6 Pages: 65201-65201

    • DOI

      10.1088/1751-8113/47/6/065201

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields2013

    • Author(s)
      KANKI, Masataka
    • Journal Title

      Journal of Nonlinear Mathematical Physics

      Volume: 20 Supplement 1 Issue: Supplement 1 Pages: 101-109

    • DOI

      10.1080/14029251.2013.862437

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete integrable equations over finite fields2012

    • Author(s)
      KANKI, Masataka
    • Journal Title

      SIGMA

      Volume: 8 Pages: 1-12

    • DOI

      10.3842/sigma.2012.054

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete Painleve II equation over finite fields2012

    • Author(s)
      KANKI, Masataka
    • Journal Title

      J. Phys. A : Math. Theor.

      Volume: 45 Issue: 34 Pages: 1-8

    • DOI

      10.1088/1751-8113/45/34/342001

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Soliton Solutions of a Generalized Discrete KdV Equation2012

    • Author(s)
      KANKI, Masataka
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 81 Issue: 8 Pages: 1-5

    • DOI

      10.1143/jpsj.81.084002

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete Integrable Equations over Finite Fields2012

    • Author(s)
      Masataka Kanki, Jun Mada, Tetsuji Tokihiro
    • Journal Title

      SIGMA

      Volume: 8 Pages: 54-54

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Discrete Painleve II equation over finite fields2012

    • Author(s)
      Masataka Kanki, Jun Mada, K M Tamizhmani, Tetsuji Tokihiro
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 45 Pages: 342001-342001

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Soliton Solutions of a Generalized Discrete KdV Equation2012

    • Author(s)
      Masataka Kanki, Jun Mada, Tetsuji Tokihiro
    • Journal Title

      Phys. Soc. Jpn.

      Volume: 81 Pages: 84002-84002

    • NAID

      40019379876

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 離散可積分系の特異点閉じ込めと互いに素条件について2014

    • Author(s)
      神吉 雅崇,時弘 哲治,間瀬 崇史,間田 潤
    • Organizer
      日本応用数理学会
    • Place of Presentation
      京都大学
    • Year and Date
      2014-03-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] p 進数体を用いた有限体上の可積分系の構成2013

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] ソリトン系の特異点閉じ込めと法p 還元について2013

    • Author(s)
      神吉 雅崇,間田 潤,時弘 哲治
    • Organizer
      日本応用数理学会
    • Place of Presentation
      アクロス福岡
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] p 進数体上の離散KdV 方程式2013

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本応用数理学会
    • Place of Presentation
      東洋大学
    • Year and Date
      2013-03-14
    • Related Report
      2013 Final Research Report
  • [Presentation] ソリトン系の特異点閉じ込めと法p還元について2013

    • Author(s)
      神吉 雅崇,間田 潤,時弘 哲治
    • Organizer
      日本応用数理学会
    • Place of Presentation
      アクロス福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] p進数体を用いた有限体上の可積分系の構成2013

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 可逆エレメンタリーセルオートマトンの相互相関行列の解析2012

    • Author(s)
      金子勇治,時弘哲治,間田潤
    • Organizer
      日本物理学会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2012-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] 有限体上の可積分方程式系について2012

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 有限体上の離散可積分系とそのソリトン解2012

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本応用数理学会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-03-09
    • Related Report
      2013 Final Research Report
  • [Presentation] 可逆エレメンタリーセルオートマトンの相互相関行列の解析

    • Author(s)
      金子勇治,時弘哲治,間田潤
    • Organizer
      日本物理学会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 有限体上の離散可積分系とそのソリトン解

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本応用数理学会
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 有限体上の可積分方程式系について

    • Author(s)
      神吉 雅崇,時弘 哲治,間田 潤
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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