| Project/Area Number |
10440057
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
SATSUMA Junkichi The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (70093242)
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| Co-Investigator(Kenkyū-buntansha) |
YANO Koichi Aoyama Gakuin University, College of Science and Engineering, Professor, 理工学部, 教授 (60114691)
OKAMOTO Kazuo The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (40011720)
TOKIHIRO Tetsuji The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (10163966)
OHTA Yasuhiro Hiroshima University, Graduate School of Engineering, Assistant Professor, 大学院・工学研究科, 助手 (10213745)
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| Project Period (FY) |
1998 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥10,500,000 (Direct Cost: ¥10,500,000)
Fiscal Year 2001: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2000: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1999: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Soliton / Integrable System / Difference Equation / Ultra-discretization / Singularity Confinement / Painleve Equation / 戸田方程式 |
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| Research Abstract |
For the purpose of clarifying the structure of "singularity confinement", extending the concept to ultra-discrete system, and revealing algebraic and geometrical structure of discrete integrable systems, we have obtained the following results.
(1) We have shown the algebraic structure of solution method for nonautonomous discrete integrable systems and constructed solutions expressed by special functions for the systems. We have also proposed new nonlinear relations among the solutions.
(2) For some discrete Painleve equations, we have clarified their self-duality and the structure of nonlinear relations among the solutions.
(3) We have obtained an ultra-discrete version of the Toda molecule equation and the explicit expression of its solutions. We have also studied its algebraic structure and symmetry, and discussed a possibility of applying the system to the field of mathematical engineering.
(4) By considering a nonlinear integro-differential equation as a difference-differential equation, we have studied its integrable structure. We have also studied the structure of solutions for a discrete analogue of coupled nonlinear wave equations.
(5) We have presented a geometrical approach to the equation which satisfies the singularity confinement criterion but exhibits chaotic behaviour. We have also given a method to caluculate the algebraic entropy by using the theory of intersection numbers.
(6) We have studied geometrical structure of the discrete Painleve equations and shown the relation between the solution space of Toda lattice equation and the solutions of discrete Painleve equations.
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