• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on algebraic structures of ultradiscrete soliton equations and applications to engineering

Research Project

Project/Area Number 13640212
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionOsaka University

Principal Investigator

NAGAI Atsushi  Nihon University, College of Industrial Technology, Lecturer, 基礎工学研究科, 助手 (90304039)

Co-Investigator(Kenkyū-buntansha) KONDO Koichi  Doshisha University, Department of Engineering, Lecturer, 工学部, 講師 (30314397)
TSUJIMOTO Satoshi  Kyoto University, Graduate School of Informatics, Lecturer, 大学院・情報学研究科, 講師 (60287977)
OKADO Masato  Osaka University, Graduate School of Engineering Science, Associate Professor, 大学院・基礎工学研究科, 助教授 (70221843)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsbox and ball systems / integrable system / discrete, ultradiscrete / fractional derivative / MIttag-Leffler function / Green function / inverse ultradiscretization / RI chain / q差分 / 非整数階微分、差分 / 可解格子模型 / 離散 / 超離散 / ソリトン / クリスタル / ソリトンセルオートマトン / 保存量 / 4階微分方程式 / パフィアン
Research Abstract

The purpose of this research is to find algebraic and analytical structures of differential, difference and ultradiscrete equations, and to apply, the mathematical results to the field of engineering. The main results obtained are as follows.
1. We have found conserved quantities of box and ball systems with arbitrary box capacities by making use of ultradiscrete KdV and Lotka-Volterra equation including their modified version.
2. We have obtained piecewise linear equation of combinatorial R of crystals associated with D type affine Lie algebra by employing inverse ultra-discretization.
3. A discrete integrable system called the RI chain, which is considered as a generalization of the Toda equation, is studied. In particular, we have obtained its bilinear form and its determinant solution. The relation with relativistic Toda equation is also found.
4. We have obtained discrete and q-discrete versions of fractional derivative together with ite eigen function called the Mittag-Leffler function. We have also constructed a new integrable mapping with fractional difference.
5. We have found Green and Poisson functions for a biharmonic operator on a disk. Their integral representations are also found.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] A.Nagai: "An integrable mapping with fractional difference"J.Phys.Soc.Jpn.. 72. 2181-2183 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nagai: "On a certain fractional q-difference and its eigen function"J.Nonl.Math.Phys.Suppl.. 10-2. 133-142 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Okado, A.Schilling, M.Shimozono: "A tensor product theorem related to perfect crystals"J.of Alg.. 267. 212-245 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Kuniba, M.Okado, T.Takagi, Y.Yamada: "Geometric crystal and tropical R for D _n^(1)"Internat.Math.Res.Notices. 48. 2565-2620 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.NIshizawa, Y.Ohta, S.Tsujimoto: "Some aspects of Toda molecule"Glasgow Math.J.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Mukaihira, S.Tsujimoto: "Determinant structure of RI type discrete integrable system"J.Phys.A. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nagai: "An integrable mapping with fractional difference"J.Phys.Soc.Jpn.. 72. 2181-2183 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nagai: "On a certain fractional q-difference and its eigen function"J.Nonl.Math.Phys.. 10 Suppl.2. 133-142 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Okado, A.Schilling, M.Shimozono: "A tensor product theorem related to perfect crystals"J.of Alg.. 267. 212-245 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Kuniba, M.Okado, T.Takagi, Y.Yamada: "Geomatric crystal and tropical R for D_n^(l)"Internat.Math.Res.Notices. 48. 2565-2620 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Nishizawa, Y.Ohta, S.Tsujimoto: "Some aspects of Toda molecule"Glasgow Math.J.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A Mukaihira, S.Tsujimoto: "Determinant structure of RI type discrete intagrable system"J.Phys.A. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nagai: "An integrable mapping with fractional difference"Journal of the Physical Society of Japan. 72. 2081-2083 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Nagai: "On a certain fractional q-difference and its eigen function"Journal of the Nonlinear Mathematical Physics. 10. 142-151 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 永井 敦: "ミッタークレフラー関数の差分化-非整数階差分とは?"数理科学. 483. 50-55 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Okado: "Virtual crystals and Kleber's algorithm"Commun.Math.Phys.. 238. 187-209 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Okado: "Geometric crystal and tropical R for D^{(1)}_n"Internat.Math.Res.Notices. 48. 2565-2620 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Nagai: "Discrete Mittag-Leffler function and its applications"数理解析研究所講究録. 1302. 1-20 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 亀高惟倫, 竹居賢治, 永井 敦: "円板内の重調和作用素に対するグリーン関数とポアッソン関数"数理解析研究所講究録. 1302. 60-67 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] G.Hatayama, A.Kuniba, M.Okado, T.Takagi: "Combinatorial R matrices and a family of crystals B ^<(1)>_n, D^<(1)>_n, A^<(2)>_<2n> and D^<(2)>_<n+1> cases"Journal of Algebra. 247. 577-615 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] G.Hatayama, A.Kuniba, M.Okado, T.Takagi, Y.Yamada: "Scattering rules in soliton cellular automata associated with crystal bases"Comtemporary Mathematics. 297. 151-182 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Tsujimoto: "On a Discrete Analogue of the Two-Dimensional Toda Lattice Hierarchy"Publication RIMS Kyoto University. 38. 113-133 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kondo, Y.Nakamura: "Determinantal solutions of solvable chaotic systems"J. Comp. Appl. Math.. 145. 361-372 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Nagai, T.Tokihiro, J.Satsuma: "Conserved quantities of box and ball systems"Glasgow Mathematical Journal. 43A. 91-98 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kametaka, K.Takemura, Y.Suzuki, A.Nagai: "Positivity and hierarchical structure of Green's functions of 2-point Boundary value problems for bending of a beam"Japan Journal of Industrial and Applied Mathematics. 18. 543-566 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Okado, A.Schlling, M.Shimozono: "Crystal bases and q-identities"Comtemporary Mathematics. 291. 29-53 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] G.Hatayama, A.Kuniba, M.Okado, T.Takagi: "Combinatorial R matrices for a family of crystals : B^<(1)>_n, D^<(1)>_n, A^<(2)>_<2n>, and D^<(2)>_<n+1> cases"Journal of Algebra. 247. 577-615 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] C.R.Gilson, J.J.C.Nimmo, S.Tsujimoto: "Pfaffianization of the discrete KP equation"Journal of Physics A. 34. 10569-10576 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] R.Hirota, M.Iwao, S.Tsujimoto: "Soliton equations exhibiting Pfaffian solutions"Glasgow Mathematical Journal. 43A. 33-42 (2001)

    • Related Report
      2001 Annual Research Report

URL: 

Published: 2001-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi