A Geometrical Description¶of the Discrete Painlevé VI and V Equations
A Geometrical Description¶of the Discrete Painlevé VI and V Equations
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离散 Painlevé VI 和 V 方程的几何描述¶
DOI：
10.1007/s002200100361
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发表时间：
2001
影响因子：
2.4
通讯作者：
Y. Ohta
中科院分区：
文献类型：
--
作者：
A. Ramani;B. Grammaticos;Y. Ohta
提出了一种基于Weyl群的离散Painlevé方程的几何方法。该方法依赖于双线性形式主义，并假设多维τ-函数生活在适当的仿射Weyl群的权格上。τ函数的方程是一个非自治的Hirota-Miwa方程组，它控制着方程的独立变量和参数的沿着演化（后者由Schlesinger变换引起）。本文分析了E（1）7群的情形。利用几何描述，我们推导出非线性离散方程。我们发现，在E（1）7群的情况下，这些是最近提出的“不对称“q-PVI和d-PVI。
We present a geometrical approach for the discrete Painlevé equations based on Weyl groups. The method relies on the bilinear formalism and assumes that the multidimensional τ-function lives on the weight lattice of the appropriate affine Weyl group. The equations for the τ-function, a system of nonautonomous Hirota–Miwa equations, govern the evolution along the independent variable and the parameters of the equation (the latter evolution induced by the Schlesinger transformations). In the present paper we analyse the case of the E(1)7group. Using the geometrical description we derive the nonlinear discrete equations. We find that in the case of the E(1)7group these are the “asymmetric”q-PVIand d-PVthat were recently proposed.
影响因子：
2.4
作者：
H. Sakai
通讯作者：
H. Sakai