A Geometrical Description¶of the Discrete Painlevé VI and V Equations

被引：0
|
作者：
A. Ramani
B. Grammaticos
Y. Ohta
机构：
[1] CPT,
[2] Ecole Polytechnique,undefined
[3] CNRS,undefined
[4] UMR 7644,undefined
[5] 91128 Palaiseau,undefined
[6] France,undefined
[7] GMPIB,undefined
[8] Université Paris VII,undefined
[9] Tour 24-14,undefined
[10] 5e étage,undefined
[11] case 7021,undefined
[12] 75251 Paris,undefined
[13] France,undefined
[14] Department of Applied Mathematics,undefined
[15] Faculty of Engineering,undefined
[16] Hiroshima University,undefined
[17] 1-4-1 Kagamiyama,undefined
[18] Higashi-Hiroshima 739-8527,undefined
[19] Japan,undefined
来源：
Communications in Mathematical Physics | 2001年 / 217卷
关键词：
Bilinear Formalism; Weyl Group; Geometrical Approach; Versus Equation; Discrete Equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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)7 group. Using the geometrical description we derive the nonlinear discrete equations. We find that in the case of the E(1)7 group these are the “asymmetric”q-PVI and d-PV that were recently proposed.
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页码：315 / 329
页数：14
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