Self-Duality and Schlesinger Chains for the Asymmetric d-PII and q-PIII Equations
Self-Duality and Schlesinger Chains for the Asymmetric d-PII and q-PIII Equations
复制标题
非对称 d-PII 和 q-PIII 方程的自对偶性和施莱辛格链
DOI：
10.1007/s002200050291
复制
发表时间：
1998
影响因子：
2.4
通讯作者：
B. Grammaticos
中科院分区：
文献类型：
--
作者：
A. Ramani;Y. Ohta;J. Satsuma;B. Grammaticos
翻译后摘要：我们分析两个不对称的离散Painlevé方程，即d-PII和q-PIII这是已知的PIII和PVI分别是离散形式。我们证明了这两个方程都是自对偶的。这意味着相同的方程支配沿着离散自变量的演化，并且在Schlesinger变换的作用下沿着沿着离散Painlevé的参数进行变换。一个双线性制定的自对偶方程作为一个系统的非自治Hirota-Miwa方程。
Abstract:We analyse two asymmetric discrete Painlevé equations, namely d-PII and q-PIII which are known to be discrete forms of PIII and PVI respectively. We show that both equations are self-dual. This means that the same equation governs the evolution along the discrete independent variable and the transformations under the action of the Schlesinger transforms along the parameters of the discrete Painlevé. A bilinear formulation of the self-dual equation is given as a system of nonautonomous Hirota–Miwa equations.