Construction of special solutions to Painleve systems and the quest for infinite-dimensional integrable systems
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：
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
项目状态：
已结题
起止时间：
2009 至 2012
中文摘要
翻译
我们构造了离散Painleve系统的几个特殊解。我们完整地确定了解的tau函数，并从仿射Weyl群对称的角度对作为解的函数的一些性质进行了自然的描述。我们还根据第6个Painlve方程的超几何型解构造了离散幂函数的显式公式。此外，我们试图构造高阶Painleve系统的离散模拟和特殊解，为发现新的无限维可积系统铺平道路
英文摘要
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
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
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
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
影响因子：
--
作者：
[Hisashi Ando, Mike Hay, Kenji Kajiwara and Tetsu Masuda]
通讯作者：
Kenji Kajiwara and Tetsu Masuda
A Generalization of the Painlev'e systems to higher dimension, their special solutions, symmetries and relations to integrables systems
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批准号：18740090
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项目类别：Grant-in-Aid for Young Scientists (B)
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资助金额：$2.39万
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财政年份：2006
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负责人：MASUDA Tetsu
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依托单位：