Study on the integrable structure of ultradiscrete systems

超离散系统可积结构研究

• 批准号: 21340034
• 负责人: TOKIHIRO Tetsuji
• 金额: $ 10.07万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2013-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21340034/
• 关键词: セルオートマトン; 超離散系; 可積分系; 箱玉系; 有限体; トロピカル曲線; 特異値閉じ込め; トロピカル; ソリトン

An ultradiscrete system denotes a cellular automaton constructed from a continuous equation through a limiting procedure. We investigated the ultradiscrete systems which are considered to have integrability. The principal results in this research are; (1) the correlation functions of the box-ball systems, which are typical integrable ultrtadiscrete systems, are obtained, (2) the mathematical structure of the so-called negative solitons in the ultradiscrete KdV equation is clarified, (3) solutions to ultradiscrete Painlevé equations are constructed and a series of formulae for partition numbers are obtained, (4) integrable systems over finite fields are shown to have a property called AGR (almost good reduction).

超离散系统是指由一个连续方程通过一个极限过程构造的元胞自动机。研究了被认为具有可积性的超离散系统。本研究的主要结果是：(1)得到了典型的可积超分散系统--箱球系统的关联函数；(2)阐明了超离散KdV方程中所谓负孤子的数学结构；(3)构造了超离散Painlevé方程的解，得到了一系列分拆数公式；(4)证明了有限域上的可积系统具有一种称为AGR(几乎良好约化)的性质。

项目成果

The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields

有限域上离散Painleve II方程的初始条件空间和几乎良好约简的性质

• DOI: 10.1080/14029251.2013.862437
• 发表时间: 2013
• 期刊: Journal of Nonlinear Mathematical Physics
• 影响因子: 0.7
• 作者: KANKI;Masataka
• 通讯作者: Masataka

Solution to the initial value problem of the ultradiscrete periodic Toda equation

超离散周期Toda方程初值问题的求解

• 发表时间: 2009
• 期刊: J.Phys.A : Math.Theor. 42
• 作者: 岩根秀直;樋口博之;穴井宏和;Seiya Negami;Rei-ichiro KAWAI;J. Byeon and K. Tanaka;M.Idzumi
• 通讯作者: M.Idzumi

Two point correlation functions for a periodic box-ball system

周期性盒球系统的两点相关函数

• DOI: 10.3842/sigma.2011.027
• 发表时间: 2011
• 期刊: SIGMA
• 作者: Justin Bush;Marcio Gameiro;Shaun Harker;Hiroshi Kokubu;Konstantin Mischaikow;Ippei Obayashi;Pawel Pilarczyk;J. Mada and T. Tokihiro
• 通讯作者: J. Mada and T. Tokihiro

FOLDING TRANSFORMATIONS AND HKY MAPPINGS

折叠变换和 HKY 映射

• DOI: 10.1142/s1402925111001179
• 发表时间: 2011
• 期刊: Journal of Nonlinear Mathematical Physics
• 影响因子: 0.7
• 作者: B. GRAMMATICOS;A. RAMANI and R. WILLOX
• 通讯作者: A. RAMANI and R. WILLOX

Integrable Equations over Finite Fields

有限域上的可积方程

• 发表时间: 2013
• 作者: B.-F.Feng;J.Inoguchi;K.Kajiwara;K.Maruno and Y.Ohta;穴井宏和;Y. Takei;仲田均;Seiya Negami;時弘哲治
• 通讯作者: 時弘哲治