Grant-in-Aid for international Scientific Research
|Allocation Type||Single-year Grants |
|Research Institution||University of Tokyo |
WADATI Miki Graduate School of Science, Univ.of Tokyo, Professor, 大学院・理学系研究科, 教授 (60015831)
SEGUR Harvey Program in Applied Mathematics, Univ.of Colorado, Professor, 応用数学, 教授
ABLOWITZ Mark Program in Applied Mathematics, Univ.of Colorado, Professor, 応用数学, 教授
NAGAO Taro Faculty of Science, Univ.of Osaka, Research Associate, 理学部, 助手 (10263196)
HIKAMI Kazuhiro Graduate School of Science, Univ.of Tokyo, Research Associate, 理学系・研究科, 助手 (60262151)
IIZUKA Takeshi Faculty of Science, Univ.of Ehime, Research Associate, 理学部, 助手 (10263922)
DEGUCHI Tetsuo Faculty of Science, Univ.of Ochanomizu, Assistant Professor, 理学部, 助教授 (70227544)
YAJIMA Tetsu Graduate School of Engineering, Univ.of Tokyo, Research Associate, 工学部, 助手 (40230198)
SEGUR H. コロラド大学, 応用数学, 教授
ABLOWITZ M.J コロラド大学, 応用数学, 教授
|Project Period (FY)
1994 – 1995
Completed (Fiscal Year 1995)
|Budget Amount *help
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 1995: ¥4,300,000 (Direct Cost: ¥4,300,000)
Fiscal Year 1994: ¥4,100,000 (Direct Cost: ¥4,100,000)
|Keywords||Soliton / Integrable system / Inverse scattering method / Yangian / Geometrical model / Quanturi integrable system / Nonlinear wave / Discrete integrable system / Nonlinear Schrodinger equation / 光ソリトン / W-代数 / カロジェロ系 / ヤン・バクスター関係式 / 面の運動|
Theory and Applications of Nonlinear Dynamical Systems
In this project.a main theme is the analysis of nonlinear dynamical systems with large degrees of freedom which appear in various fields of physics. The followings are summary of the results.
1. Quantum integrable systems with long-range interactions
We have developped the quantum inverse scattering method for onedimensional quantum particle systems with long-range interactions. Integrabilities of the Calogero-Moser model and the Sutherland model are proved. Those models are extended so as to include internal degrees of freedom (spins). The Dunkl operator approach and the exchange operator approach are also clarified.
2. Geometrical models
The purposes are two folds. One is the extension of the soliton systems to higher-dimensional ones and the other is a general setting for descriptions of geometrical objects in physics. We have developped the level-set formulation of the surfaces in arbitrary space-dimension. Special solutions of the curve-lengthening equation which generalize the Saffman-Taylor finger solution are found.
3. Discrete dynamical models
The geometrical models are extended into the discrete curves and the discrete surfaces. The relations with descrete integrable systems (the discrete Modified K-dV hierarchy) are found.
4. Two-dimensional integrable systems
The Davey-Stewartson equation which is considered to be a two-dimensional extension of the nonlinear Schrodinger equation is studied numerically. The stability of dromions and the role of the mean flows are clarified.
5. Random Knotting
As a model for polymers, topological configurations of random walks are investigated. Probability of a knot K as a function of the length N.P (K.N).is determined by numerical experiments. The proposed formula for B (K.N) agrees well with the numerical results.