Geometric description of a discrete power function associated with the sixth Painlev? equation
Geometric description of a discrete power function associated with the sixth Painlev? equation
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与第六 Painlev 相关的离散幂函数的几何描述？
DOI：
10.1098/rspa.2017.0312
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Shi Yang
中科院分区：
文献类型：
--
作者：
Joshi Nalini;Kajiwara Kenji;Masuda Tetsu;Nakazono Nobutaka;Shi Yang
本文考虑与第六类Painlevé方程相关的离散幂函数。该函数是具有相似约束的所谓交叉比方程的特解。本文证明了该系统嵌入到具有对称性的立方晶格中。通过构造的作用作为的子群，即PVI的对称群，我们展示了如何与晶格的对称群相联系。此外，通过使用中的平移，我们用τ函数解释了以前已知的显式中出现的奇偶结构。
In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice withsymmetry. By constructing the action ofas a subgroup of, i.e. the symmetry group ofPVI, we show how to relateto the symmetry group of the lattice. Moreover, by using translations in, we explain the odd–even structure appearing in previously known explicit formulae in terms of theτfunction.