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1991 Fiscal Year Final Research Report Summary

Exactly Solvable Models and Applications

Research Project

Project/Area Number 01540310
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionUniversity of Tokyo

Principal Investigator

WADATI Miki  University of Tokyo Department of Physics Professor, 理学部, 教授 (60015831)

Project Period (FY) 1989 – 1991
KeywordsSoliton / Yang-Baxter Relation / Exactly solvable Model / Unstable Nonlinear Schrodinger Equation / Knot Theory / Link Polynomial / Random Media / Finite Temperature Baxter's Formula
Research Abstract

1) We extend the theory of soliton to the analysis of non-linear waves in unstable physical system. The unstable Nonlinear Schrodinger (UNLS) equation is introduced, whereby propagation of. a localized mode in electron-beam plasma is explained. In addition, a new nonlinear evolution. equation which encompass chaos and soliton phenomena is proposed.
2) We investigate the solillo-n propagations under external noise and in radom media. Using a one-dimensional lattice with radom mass distribution, we clarify the localized wave propagations and the modulations of plane waves.
3) We extend the Baxter's formula which relates 2-D statistical mechanical model and 1-D quatum system into finite temperature case. Combining this extension with the theory of finite size corrections, we evaluate the free energies and the covelation lengths of quantum spin systems.
4) We develop a general theory to obtain link polgnomials from exactly solvable models in 2-D statistical mechanics. Applying the theory. to various model, we get new link polynomials and the known link polynomials. This theory may play an important role not only in recent mathematical' physics but also in quatum gravitation theory.

  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] M.WADATI: "Old and New Link Polynomials from the Theory of Exactly Solvable Models" Physica D. 51. 376-387 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.WADATI: "Solition Phenomana in Unstable Media" Physica D. 51. 388-406 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.WADATI: "The Unstable Nonlinear Schrodinger Equation;The Theory and its Applications" Chaos,Solition and Fractal. 1. 149-271 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.IIZUKA: "Propagation of Solitons in Random Lattices" J.Phys.Soc.Jpn.60. 4167-4174 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.WADATI: "A New Hamiltonian Ampletude Equation Governing Modulated Wave Instability" J.Phys.Soc.Jpn.61. (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.SUZUKI: "Exactiy Solvable Models and Finite Size Corrections" International Modern Physics. (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.WADATI: "Proceedings of the 25th International Conference on High Energy Physics,Vol.2,pp.1389-1398" World Scientific Publishing ed.by K.K.Phua and Y.Yamaguchi, 11 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.IIZUKA: "Nonlinear Dispersive Waves" World Scientific Publising ed.by L.Debnath, (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Wadati and T. Deguchi: "Old and New Link Polynomials from the Theory of Exactly solvable Models" Physica D. 51. 376-387 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Wadati, T. Iizuka and T. Yajima: "Soliton Phenomena in Unstable Media" Physica D. 51. 388-406 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Wadati: "Deformation of solitons in Random Media" J. Phys. Soc. Jpn.59. 4201-4203 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Iizuka, M. Wadati and T. Yajima: "the Unstable Schrodinger Equation and Dark Solitons" J. Phys. Soc. Jpn.60. 2862-2875 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Mori, K. Kaneko and M. Wadati: "Fracture Dynamics by Quenching. I. Crack Patterns" J. Phys. Soc. Jpn.60. 1591-1599 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Iizuka, T. Nakao and M. wadati: "Propagation of solitons in Random Lattices" J. Phys. Soc. Jpn.60. 4167-4174 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Wadati, T. Yajima and T. Iizuka: "The Unstable Nonlinear Schrodinger Equation, The Theory and its Applications" Chaos, Soliton and Fractal. 1. 249-271 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Wadati, H. Segur and M. J. Ablowitz: "A New Hamiltonian Amplitude Equation Governing Modulated Wave Instability]" J. Phys. Soc. Jpn.61. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J. Suzuki, T. Nagao and M. Wadati: "Exactly Solvable Models and Finite Size Corrections" International Modern Physics. (1992)

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

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Published: 1993-03-16  

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