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2003 Fiscal Year Final Research Report Summary

Integrable systems with higher genus spectral parameter

Research Project

Project/Area Number 14540172
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

TAKASAKI Kanehisa  Kyoto Univ., Graduate School of Human and Environmental Studies, Professor, 大学院・人間・環境学研究科, 教授 (40171433)

Co-Investigator(Kenkyū-buntansha) SASAKI Ryu  Kyoto Univ., Yukawa Institute for Theoretical Physics, Ass.Professor, 基礎物理学研究所, 助教授 (20154007)
TAKEBE Takashi  Ochanomizu Women's University, Department of Mathematics, Ass.Professor, 理学部, 助教授 (60240727)
IKEDA Takeshi  Okayama Science University, Department of Applied Mathematics, Lecture, 理学部, 講師 (40309539)
UEKI Naomasa  Kyoto Univ., Graduate School of Human and Environmental Studies, Ass.Professor, 大学院・人間・環境学研究科, 助教授 (80211069)
UE Masaaki  Kyoto Univ., Graduate School of Science, Ass.Professor, 大学院・理学研究科, 助教授 (80134443)
Project Period (FY) 2002 – 2003
Keywordsintegrable system / soliton equation / algebraic curve / higher genus / vector bundle / Tyurin parameter / Grassmann manifold
Research Abstract

There has been progress in several different aspects as follows.
1.Soliton equations related to Tyurin parameters: Following Krichever's recent proposal on a construction of integrable systems with Tyurin parameters, we constructed an elliptic analogue of the nonlinear Schroedinger equation. It turned out that this equation, like many other soliton equations, can be mapped to a dynamical system on a submanifold of an infinite dimensional Grassmann manifold. This result result can be to an algebraic curve of arbitrary genus.
2. Landau-Lifshitz equation and infinite dimensional Grassmann variety: The Landau-Lifshitz equation is a typical soliton equation related to an elliptic curve. We found that this equation, too, can be interpreted as a dynamical system on a submanifold of an infinite dimensional Grassmann manifold.
3.Integrable system formulated by a pair of meromorphic functions on an algebraic curve of arbitrary genus: We constructed an integrable system on the moduli space of a pair of meromorphic functions on an algebraic curve of arbitrary genus. This system may be thought of as a special case of the so called Beauville system.

  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] 高崎金久: "Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains"Communications in Mathematical Physics. 241巻1号. 111-142 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 高崎金久: "Landau-Lifshitz hierarchy and infinite dimensional Grassmann variety"Letters in Mathematical Physics. (未定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 武部尚志: "Trigonometric degeneration and orbifold Wess-Zumino-Witten model, I"Journal of Modern Physics A. (未定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐々木 隆, 他: "Eigenvalues of Ruijsenaars-Schneider models associated with A(n-1) root system in Bethe ansatz formalism"Journal of Mathematical Physics. 45巻. 559-575 (2004)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐々木 隆, 他: "Exact solution of Z(n) Belavin model with open boundary condition"Nuclear Physics B. 679巻. 495-520 (2004)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kanehisa Takasaki: "Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains"Communications in Mathematical Physics. vol.241. 111-142 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kanehisa Takasaki: "Landau-Lifshitz hierarchy and infinite dimensional Grassmann variety."Letters in Mathematical Physics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Takebe: "Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model.I."Journal of Physics A. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryu Sasaki et al.: "Eigenvalues of Ruijsenaars-Schneider models associated with A (n-1) root system in Bethe ansatz formalism."Journal of Mathematical Physics. vol.45. 559-575 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryu Sasaki et al.: "Exact solution of Z(n) Belavin model with open boundary condition."Nuclear Physics B. vol.679. 495-520 (2004)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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