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Bilinear method for multi-component coupled integrable systems

Research Project

Project/Area Number 24340029
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Global analysis
Research InstitutionKobe University

Principal Investigator

Ohta Yasuhiro  神戸大学, 理学研究科, 教授 (10213745)

Co-Investigator(Renkei-kenkyūsha) YAMADA Yasuhiko  神戸大学, 大学院理学研究科, 教授 (00202383)
NOUMI Masatoshi  神戸大学, 大学院理学研究科, 教授 (80164672)
Project Period (FY) 2012-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords結合型可積分系 / 双線形化法 / ソリトン / 可積分系 / 内部自由度 / rogue wave / Davey-Stewartson方程式
Outline of Final Research Achievements

For the integrable evolution equations, there are several methods to generalize them to the coupled systems of equations keeping the integrability, and those integrable coupled equations admit various types of solutions with many internal freedoms. It is important to study the multi-component coupled systems and their solutions systematically both in theoretical study and applications of integrable systems. Based on the theory of bilinear method in the classical integrable systems, the way of constructing new multi-component coupled integrable systems is proposed, and various types of interactions are described by using the internal freedoms of the solutions.

Report

(7 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (18 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (10 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 10 results,  Acknowledgement Compliant: 3 results,  Open Access: 1 results) Presentation (7 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Int'l Joint Research] The University of Texas(米国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation2017

    • Author(s)
      Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta
    • Journal Title

      Studies in Applied Mathematics

      Volume: 136 Issue: 3 Pages: 343-367

    • DOI

      10.1111/sapm.12159

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] An integrable semi-discrete Degasperis-Procesi equation2017

    • Author(s)
      B.-F. Feng, K. Maruno and Y. Ohta
    • Journal Title

      Nonlinearity

      Volume: 30 Issue: 6 Pages: 2246-2267

    • DOI

      10.1088/1361-6544/aa67fc

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Degasperis-Procesi equation, its short wave model and the CKP hierarchy2017

    • Author(s)
      B.-F. Feng, K. Maruno and Y. Ohta
    • Journal Title

      Annal. Math. Sci. Appl.

      Volume: 2 Issue: 2 Pages: 285-316

    • DOI

      10.4310/amsa.2017.v2.n2.a4

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] N-bright-dark soliton solution to a semi-discrete vector nonlinear Schroedinger equation2017

    • Author(s)
      B.-F. Feng and Y. Ohta
    • Journal Title

      SIGMA Symmetry Integrability Geom. Methods Appl.

      Volume: 13 Pages: 071-071

    • DOI

      10.3842/sigma.2017.071

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue2017

    • Author(s)
      B.-F. Feng, K. Maruno and Y. Ohta
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 50 Pages: 055201-055201

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] From the real and complex coupled dispersionless equations to the real and complex short pulse equations2016

    • Author(s)
      S. Shen, B.-F. Feng and Y. Ohta
    • Journal Title

      Stud. Appl. Math.

      Volume: 136 Pages: 64-88

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Integrable semi-discretization of a multi-component short pulse equation2015

    • Author(s)
      B.-F. Feng, K. Maruno and Y. Ohta
    • Journal Title

      J. Math. Phys.

      Volume: 56 Pages: 043502-043502

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Discrete mKdV and discrete sine-Gordon flows on discrete space curves2014

    • Author(s)
      J. Inoguchi, K. Kajiwara, N. Matsuura and Y. Ohta
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 47 Pages: 235202-235202

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Integrable Discretizations of the Dym Equation2013

    • Author(s)
      B.-F. Feng, J. Inoguchi, K. Kajiwara, K. Maruno and Y. Ohta
    • Journal Title

      Front. Math. China

      Volume: 8 Pages: 1017-1029

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of rogue waves in the Davey-Stewartson II equation2013

    • Author(s)
      Y. Ohta, et al.
    • Journal Title

      J. Phys. A : Math. Theor.

      Volume: 46 Pages: 105-202

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Semi-discrete analogues of the complex short pulse and coupled complex short pulse equations based on the KP hierarchy reduction2017

    • Author(s)
      Baofeng Feng and Yasuhiro Ohta
    • Organizer
      AMS Sectional Meeting (Fall Central Sectional Meeting)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Coupled soliton equations derived from BKP hierarchy by reduction2015

    • Author(s)
      Y. Ohta
    • Organizer
      International Workshop on Integrable Systems -- Mathematical Analysis and Scientific Computing
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2015-10-19
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 自己適合移動格子スキームとミンコフスキー平面上の離散曲線の運動について2014

    • Author(s)
      丸野 健一, 梶原 健司, 井ノ口 順一, 太田 泰広, Feng Baofeng
    • Organizer
      日本応用数理学会2014年度年会
    • Place of Presentation
      東京
    • Year and Date
      2014-09-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] 離散mKdV方程式と離散sine-Gordon方程式による空間離散曲線の変形2014

    • Author(s)
      井ノ口順一, 梶原健司, 松浦望, 太田泰広
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] BKP with 2-reduction2013

    • Author(s)
      Y. Ohta
    • Organizer
      China-Japan Joint Workshop on Integrable Systems 2013
    • Place of Presentation
      Kyoto, Japan(招待講演)
    • Year and Date
      2013-03-17
    • Related Report
      2012 Annual Research Report
  • [Presentation] Discrete mKdV flow on discrete space curves2013

    • Author(s)
      井ノ口順一, 梶原健司, 松浦望, 太田泰広
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] 空間離散曲線の等周変形と離散K曲面2013

    • Author(s)
      井ノ口順一, 梶原健司, 松浦望, 太田泰広
    • Organizer
      平成25年度九州大学応用力学研究所共同利用研究集会「非線形波動研究の拡がり」
    • Place of Presentation
      福岡
    • Related Report
      2013 Annual Research Report

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Published: 2012-04-24   Modified: 2022-02-21  

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