Construction of special solutions to Painleve systems and the quest for infinite-dimensional integrable systems

Painleve 系统特殊解决方案的构建以及对无限维可积系统的探索

• 批准号: 21740126
• 负责人: MASUDA Tetsu
• 金额: $ 2.58万
• 依托单位: Aoyama Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740126/
• 关键词: 可積分系; 離散羃函数; 笹野系; q-類似; タウ函数; 数理物理; 離散冪函数; 第6パンルヴェ方程式; アフィンワイル群対称性; 高次元可積分系; q-超幾何函数; q-パンルヴェ系

We constructed several special solutions to the discrete Painleve systems. We determined the tau-functions of the solutions completely, and gave a natural description for some properties of the functions that appear as the solutions from the viewpoint of the affine Weyl group symmetry. We also constructed an explicit formula for the discrete power function in terms of the hypergeometric type solutions to the sixth Painlve equation. Moreover, we tried to construct a discrete analogue and special solutions of the higer-order Painleve systems to pave the way for discovering new infinite dimensional integrable systems

我们为离散的Painleve系统构建了几种特殊解决方案。我们完全确定了溶液的tau函数，并为函数的某些属性提供了自然描述，这些功能从仿期韦伊尔组对称性的角度看作为解决方案。我们还根据第六次止痛方程的超几何类型解决方案构建了一个明确的公式。此外，我们试图构建Higer-rorder Painleve系统的离散模拟和特殊解决方案，以铺平发现新的无限尺寸可集成系统的方式

项目成果

An Explicit Formula for the Discrete Power Function Associated with Circle Patterns of Schramm Type

与Schramm型圆型相关的离散幂函数的显式公式

• DOI: 10.1619/fesi.57.1
• 发表时间: 2014
• 期刊: Funkcialaj Ekvacioj
• 作者: Hisashi Ando;Mike Hay;Kenji Kajiwara and Tetsu Masuda
• 通讯作者: Kenji Kajiwara and Tetsu Masuda