New development of discrete differential geometry by discrete integrable systems

离散可积系统离散微分几何的新发展

• 批准号: 21656027
• 负责人: KAJIWARA Kenji
• 金额: $ 1.82万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21656027/
• 关键词: 離散可積分系; 離散微分幾何; 離散ソリトン方程式; τ関数; 離散曲線; 不均一格子; 双線形形式; 離散正則関数; 超幾何関数

Discrete differential geometry has been considered, which is a mathematical framework describing the dynamics of geometric objects on computers. Theory of discrete integrable systems has been developed, which was successfully applied to discretize the planar curve dynamics on Eucledian plane and to construct explicit formulas in terms of the z functions. As by-products, highaccuracy stable numerical schemes for curve dynamics with adaptive step size control, and seeds of new development to the theory of discrete conformal mappings have been obtained.

离散微分几何被认为是在计算机上描述几何对象动力学的数学框架。发展了离散可积系统理论，成功地将其应用于欧氏平面上的平面曲线动力学的离散化，并构造了以z函数表示的显式公式。作为副产品，具有自适应步长控制的曲线动力学的高精度稳定数值格式，以及离散共形映射理论的新发展的种子已经获得。

项目成果

Bilinearization and Casorati determinant solutions to non-autonomous 1+ 1 dimensional discrete soliton equations

非自治 1 1 维离散孤子方程的双线性化和 Casorati 行列式解

• 发表时间: 2009
• 期刊: RIMS Kokyuroku Bessatu
• 作者: 海老原龍夫;小橋博道;石原隆;寺元貴幸;松本正己;早勢欣和;真鍋保彦;宇佐見仁英;川田重夫;K. Kajiwara and Y. Ohta
• 通讯作者: K. Kajiwara and Y. Ohta

Bilinearization and Casorati determinant solutions to non-autonomous 1+1 dimensional discrete soliton equations

非自治 1 1 维离散孤子方程的双线性化和 Casorati 行列式解

• 发表时间: 2009
• 期刊: RIMS Kokyuroku Bessatsu B13
• 作者: Kenji Kajiwara;Yasuhiro Ohta
• 通讯作者: Yasuhiro Ohta

Discretization of planar curve motions and discrete integrable systems

平面曲线运动的离散化和离散可积系统

• 发表时间: 2011
• 作者: Yasuhide Shindo;Takayoshi Sasakura and Fumio Narita;Dynamic;梶原健司
• 通讯作者: 梶原健司

The discrete potential Boussinesq equation and its multisoliton solutions

• DOI: 10.1080/00036810903569473
• 发表时间: 2009-08
• 期刊: Applicable Analysis
• 影响因子: 1.1
• 作者: K. Maruno;K. Kajiwara

Hirota-Satsumaの非線形ネットワーク方程式の双線形構造と解

Hirota-Satsuma非线性网络方程的双线性结构及求解

• 发表时间: 2012
• 作者: 野見山直之;梶原健司
• 通讯作者: 梶原健司