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1999 Fiscal Year Final Research Report Summary

DEVELOPMENT AND APPLICATION OF SYMPLECTIC INTEGRATOR

Research Project

Project/Area Number 09640307
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNATIONAL ASTRONOMICAL OBSERVATORY

Principal Investigator

YOSHIDA Haruo  NAO, DIVISION OF ASTROMETRY AND CELESTIAL MECHANICS, ASSOCIATE PROFESSOR, 位置天文・天体力学研究系, 助教授 (70220663)

Co-Investigator(Kenkyū-buntansha) NAKAI Hiroshi  NAO, PUBLIC RELATIONS CENTERS, RESEARCH ASSOCIATE, 天文情報公開センター, 助手 (60155653)
TANIKAWA Kiyotaka  NAO, DIVISION OF THEORETICAL ASTROPHYSICS, ASSOCIATE PROFESSOR, 理論天文学研究系, 助教授 (80125210)
Project Period (FY) 1997 – 1999
KeywordsHamiltonian dynamical system / Numerical integration method / Symplectic
Research Abstract

As for researches directly related to the main subject, simplistic integrators for infinite dimensional Hiamiltonian systems (partial differential equations) such as nonlinear Schrodinger equation have been developed. The first order scheme corresponds to "split-step quasi Fourier method" which has been known already. Higher order explicit integrators can be easily implemented, which enable us to compute fast and very accurately. In addition, the following results have been obtained in some related areas:
(1) A new necessary condition for integrability has been obtained which is based on differential Galois theory. This new necessary condition well justifies the efficiency of empirical singular point analysis.
(2) In a family of smooth mappings in a plane, general rule has been found for the appearance of homoclinic and heteroclinic points.
(3) A new knowledge has been obtained for the smoothness of KAM curve for the standard mapping. This is based on the analysis of multi-fractal.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] H. Yoshida: "A new-necessary condition for the integrability of Hamiltonian systems with a two dimensional homogeneous potential"Physica D. 128. 53-69 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Yoshida: "From sigularpoint analysis to regorous results on integrability,A dream of S.kowale*skata"Hamilton systems eith three or more de* of freedam. 270-282 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉田春夫: "微分ガロア理論による可積分性の必要条件"数理科学. 434. 41-49 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐々成正: "非線形Shodinger方程式に対するsysplectic数値解法"日本応用数理学会論文誌. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Tanikawa: "On the appearance order of homoclinic and heteroclinic intersection in a family of smooth maps of the plane"Chaos, Solitons and Fractals. 9. 1495-1512 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y. Yamaguchi: "A remark on the smoothness of KAM curue in the standard mapping"Progress of Theoretical Physics. 101. 1-24 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshida, H.: "A new necessary condition for the integrability dimensional homogeneous potential"Physica D. 128. 53-69 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshida, H.: "A dream of S.Kowalevskaya, in Hamiltonian Systems with Three or More Degrees of Freedom"(ed. C. Simo, Kluwer Academic Publishers). 270-282 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshida, H.: "Nonintegrability criterion for Hamiltonian systems (in Japanese)"BUSSEI KENKYUU. 70. 499-508 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshida, H.: "Integrable homogeneous potential systems and Schwarz triangle (in Japanese)"RIMS KOKYUUROKU. 70. 499-508 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshida, H.: "Necessary condition for integrability (in Japanese)"SUURI KAGAKU. 434. 41-49 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Sasa, N.: "Symplectic integrators for nonlinear Schrodinger equation (in Japanese)"OUYOU SUURI GAKKAI RONBUNSHI. (in press). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tanikawa, K.: "On the appearance order of homoclinic and heteroclinic intersections in a family of smooth maps of the plane"Chaos, Solitons and Fractals. 9. 1495-1512 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tanikawa, K.: "Oscillatory orbits in the planar three-body problem with equal masses"Cele. Mech. Dyn. Astron.. 70. 167-180 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mikkola, S.: "Does Kozai resonance drive CH Cygni?"Astron. J.. 116. 444-450 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yamaguchi, Y.: "A remark on the smoothness of KAM curves in the standard mapping"Prog. Theor. Phys.. 101. 1-24 (1999)

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

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Published: 2001-10-23  

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