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Analysis for integrable cellular automata by ultradiscretization method and its applications to non-integrable systems

Research Project

Project/Area Number 21760063
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionHosei University (2012)
Aoyama Gakuin University (2009-2011)

Principal Investigator

ISOJIMA Shin  法政大学, 理工学部, 准教授 (90422394)

Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords数理物理 / 可積分系 / セルオートマトン / 超離散化
Research Abstract

We proposed a procedure `ultradiscretization with parityvariables’, which is an extended version of usual ultradiscretization method. By meansof this procedure, we obtained various results on integrable cellular automata, forexample, construction of an ultradiscrete analog of the q-Painleve II equation and a classof its special solutions. We studied oscillatory solutions of ultradiscrete systems,derivation of soliton solutions to the Box and Ball system based on an algebro-geometricmethod and so on by usual ultradiscretization method. We also investigated anultradiscrete analog of the optimal velocity model and Kalman filter for apiecewise-linear system, which are non-integrable systems.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (45 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (27 results) Remarks (1 results)

  • [Journal Article] Tropical Krichever construction for the non-periodic box and ball system2012

    • Author(s)
      S. Iwao, H. Nagai and S. Isojima
    • Journal Title

      J.Phys. A: Math. Theor.

      Volume: Vol. 45, No. 39 Issue: 39 Pages: 395202-395202

    • DOI

      10.1088/1751-8113/45/39/395202

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 超離散系におけるカルマンフィルター,研究集会報告非線形波動研究の進展-現象と数理の相互作用-2012

    • Author(s)
      白瀬裕己, 礒島伸, 薩摩順吉
    • Journal Title

      九州大学応用力学研究所

      Pages: 147-152

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 符号付き超離散Bessel方程式とその特殊解につい て, 研究集会報告非線形波動研究の進展-現象と数理の相互作用-2012

    • Author(s)
      奈良崎史貴, 礒島伸, 薩摩順吉
    • Journal Title

      九州大学応用力学研究所

      Pages: 96-101

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Direct ultradiscretization of Ai and Bi functions and special solutions to Painelevé II equation2012

    • Author(s)
      S. Isojima, J. Satsuma and T. Tokihiro
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 45 Issue: 15 Pages: 155203-155203

    • DOI

      10.1088/1751-8113/45/15/155203

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion?2012

    • Author(s)
      N. Mimura, S. Isojima, M. Murata, J. Satsuma, A. Ramani, B. Gramaticos
    • Journal Title

      J. Math. Phys

      Volume: 53 Issue: 2 Pages: 23510-23510

    • DOI

      10.1063/1.3682229

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 符号付き超離散Bessel方程式とその特殊解について2012

    • Author(s)
      奈良﨑史貴, 礒島伸, 薩摩順吉
    • Journal Title

      研究集会報告「非線形波動研究の進展 -現象と数理の相互作用-」

      Volume: 23AO-S7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 超離散系におけるカルマンフィルター2012

    • Author(s)
      白瀬裕己, 礒島伸, 薩摩順吉
    • Journal Title

      研究集会報告「非線形波動研究の進展 -現象と数理の相互作用-」

      Volume: 23AO-S7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Class of Special Solutions for the Ultradiscrete Painleve II Equation2011

    • Author(s)
      S. Isojima, J. Satsuma
    • Journal Title

      SIGMA

      Volume: 7 Pages: 74-74

    • DOI

      10.3842/sigma.2011.074

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ultradiscrete PainleveII equation and a special function solution2011

    • Author(s)
      S. Isojima, T. Konno, N. Mimura, M. Murata, J. Satsuma
    • Journal Title

      J. Phys. A

      Volume: 44 Issue: 17 Pages: 175201-175201

    • DOI

      10.1088/1751-8113/44/17/175201

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularity confinement Test for ultradiscrete equations with parity variables2009

    • Author(s)
      N. Mimura, S. Isojima, M. Murata, J. Satsuma
    • Journal Title

      J. Phys. A

      Volume: 42 Issue: 31 Pages: 315206-315206

    • DOI

      10.1088/1751-8113/42/31/315206

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ultradiscrete optimal velocity model:A cellular-automaton model for traffic flow and linear instability of high-flux traffic2009

    • Author(s)
      M. Kanai, S. Isojima, K. Nishinari, T. Tokihiro
    • Journal Title

      Phys. Rev. E

      Volume: Vol.79,issue 5 Issue: 5

    • DOI

      10.1103/physreve.79.056108

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions in ultradiscrete system, in RIMS Kokyuroku Bessatsu B132009

    • Author(s)
      S. Isojima, T. Konno and J. Satsuma
    • Journal Title

      Expansion of Integrable Systems

      Pages: 85-93

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions of the ultradiscrete Sine-Gordon equation2009

    • Author(s)
      S. Isojima and J. Satsuma
    • Journal Title

      JSIAM Letters

      Volume: Vol.1 Pages: 25-27

    • NAID

      130000104492

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singularity confinement test for ultradiscrete equations with parity variables2009

    • Author(s)
      N.Mimura, et.al.
    • Journal Title

      J.Phys. A : Math. Theor. 42

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ultradiscrete optimal velocity model : A cellular-automaton model for traffic flow and linear instability of high-flux traffic2009

    • Author(s)
      M.Kanai, et. al.
    • Journal Title

      Phys.Rev.E 79

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions in ultradiscrete system2009

    • Author(s)
      S.Isojima, et. al.
    • Journal Title

      RIMS Kokyuroku Bessatsu B13

      Pages: 85-93

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions of the ultradiscrete Sine-Gordon epuation2009

    • Author(s)
      S.Isojima, et. al.
    • Journal Title

      JSIAM Letters 1

      Pages: 25-27

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 符号付き超離散 Ai 関数と制限付き分割数2013

    • Author(s)
      礒島伸, 薩摩順吉, 時弘哲治
    • Organizer
      日本数学会 2013 年度年会
    • Place of Presentation
      京都大学吉田キャンパス
    • Year and Date
      2013-03-22
    • Related Report
      2012 Final Research Report
  • [Presentation] On ultradiscretization with parity variables, China-Japan Joint Workshop on Integrable Systems 2013 (poster talk)2013

    • Author(s)
      Shin Isojima
    • Organizer
      Kyoto University
    • Place of Presentation
      Research Bldg.No.8,Kyoto,Japan
    • Year and Date
      2013-03-18
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散戸田方程式の振動解につ いて2012

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会 2012 年度年会応用可積分系OS
    • Place of Presentation
      稚内全日空ホテル
    • Year and Date
      2012-08-29
    • Related Report
      2012 Final Research Report
  • [Presentation] qAi 関数の超離散極限と分割数2012

    • Author(s)
      礒島伸, 薩摩順吉, 時弘哲治
    • Organizer
      日本応用数理学会2012年研究部会連合発表会
    • Place of Presentation
      九州大学伊都キャンパス
    • Year and Date
      2012-03-09
    • Related Report
      2012 Final Research Report
  • [Presentation] 符号付き超離散 Bessel 方程式とその特殊解について2011

    • Author(s)
      奈良崎史貴, 礒島伸, 薩摩順吉
    • Organizer
      研究集会非線形波動研究の進展-現象と数理の相互作用-
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2011-10-29
    • Related Report
      2012 Final Research Report
  • [Presentation] 符号付き超離散Bessel方程式とその特殊解について2011

    • Author(s)
      奈良崎史貴, 礒島伸, 薩摩順吉
    • Organizer
      研究集会「非線形波動研究の進展-現象と数理の相互作用-」
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2011-10-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超離散系におけるカルマンフィルター2011

    • Author(s)
      白瀬裕己, 礒島伸, 薩摩順吉
    • Organizer
      研究集会非線形波動研究の進展-現象と数理の相互作用-ポスターセッション
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2011-10-28
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散系におけるカルマンフィルター2011

    • Author(s)
      白瀬裕己, 礒島伸, 薩摩順吉
    • Organizer
      研究集会「非線形波動研究の進展-現象と数理の相互作用-」
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2011-10-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] 符号付き超離散 Painleve II 型方程式の特殊解の系列2011

    • Author(s)
      礒島伸 , 薩摩 順吉
    • Organizer
      日本数学会 2011 年度秋季総合分科会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2012 Final Research Report
  • [Presentation] 符号付き超離散Painleve II型方程式の特殊解の系列2011

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本数学会2011年度秋季総合分科会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超離散パンルヴェII型方程式の様々な特殊解系列2011

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本応用数理学会 2011 年度年会応用可積分系OS
    • Place of Presentation
      同志社大学今出川キャンパス
    • Year and Date
      2011-09-14
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散パンルヴェII型方程式の様々な特殊解系列2011

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本応用数理学会2011年度年会応用可積分系オーガナイズドセッション
    • Place of Presentation
      同志社大学今出川キャンパス
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Ultradiscrete Painleve II equation with parity variables and a class of its special function solutions2011

    • Author(s)
      Shin Isojima
    • Organizer
      The 7th IMACS International Conference on Nonlinear Evolution Equations and WavePhenomena: Computation and Theory, The University of Georgia, Center for Continuing Education
    • Place of Presentation
      Athens, Georgia, USA
    • Year and Date
      2011-04-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Ultradiscrete Painleve II equation with parity variables and a class of its special function solutions2011

    • Author(s)
      Shin Isojima
    • Organizer
      The 7th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena : Computation and Theory
    • Place of Presentation
      The University of Georgia, Center for Continuing Education (USA)
    • Year and Date
      2011-04-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超離散パンルヴェ II 型方程式の Airy 関数型の解2011

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本応用数理学会 2011 年研究部会連合発表会
    • Place of Presentation
      電気通信大学
    • Year and Date
      2011-03-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散パンルヴェII型方程式のAiry関数型の解2011

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会2011年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都)
    • Year and Date
      2011-03-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 符号付き超離散パンルヴェ II 型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸, 今野智之,三村尚之,村田実 貴生, 薩摩順吉
    • Organizer
      研究集会非線形波動研究の新たな展開-現象とモデル化-
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2010-10-30
    • Related Report
      2012 Final Research Report
  • [Presentation] 符号付き超離散パンルヴェII型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸
    • Organizer
      研究集会「非線形波動研究の新たな展開-現象とモデル化-」
    • Place of Presentation
      九州大学応用力学研究所(福岡県)
    • Year and Date
      2010-10-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之, 礒島伸,村田実貴生,薩摩 順吉,A. Ramani, B. Grammaticos
    • Organizer
      研究集会非線形波動研究の新 たな展開-現象とモデル化-
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2010-10-28
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之
    • Organizer
      研究集会「非線形波動研究の新たな展開-現象とモデル化-」
    • Place of Presentation
      九州大学応用力学研究所(福岡県)
    • Year and Date
      2010-10-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超離散パンルヴェ II 型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸, 今野智之,三村尚之,村田実 貴生,薩摩順吉
    • Organizer
      日本応用数理学会2010 年度年会ポスターセッショ ン
    • Place of Presentation
      明治大学
    • Year and Date
      2010-09-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之, 礒島伸,村田実貴生, 薩摩 順吉
    • Organizer
      日本応用数理学会2010 年度年会ポスターセッション
    • Place of Presentation
      明治大学
    • Year and Date
      2010-09-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 超離散パンルヴェII型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会2010年度年会ポスターセッション
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之
    • Organizer
      日本応用数理学会2010年度年会ポスターセッション
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超離散戸田方程式の振動解について

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会2012年度年会 応用可積分系OS
    • Place of Presentation
      稚内全日空ホテル(北海道)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 符号付き超離散Ai関数と制限付き分割数

    • Author(s)
      礒島伸, 薩摩順吉, 時弘哲治
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2012 Annual Research Report
  • [Presentation] On ultradiscretization with parity variables

    • Author(s)
      Shin Isojima
    • Organizer
      China-Japan Joint Workshop on Integrable Systems 2013 (poster talk)
    • Place of Presentation
      Kyoto University (Kyoto)
    • Related Report
      2012 Annual Research Report
  • [Remarks] 学会発表 6.はベストポスター賞を受賞。

    • Related Report
      2012 Final Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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