Degeneration of the two dimensional Gamier system
Degeneration of the two dimensional Gamier system
复制标题
二维 Gamier 系统的退化
DOI：
10.3792/pjaa.57.446
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
H. Kimura
中科院分区：
文献类型：
--
作者：
H. Kimura
(1.1)d2Y。 ---p(x t)y。 dx 他证明第六个Painlev方程只是Fuchsian型线性方程(1.1)的变形方程，其中t是变形参数。 R. Garnier [2] 将上述结果在两个方向上进行了扩展。首先，他证明了Painlev的其他五个方程可以通过具有不规则奇点的(1.1)形式的线性方程的等单向变形得到。其次，他从具有N个变形参数t=(t,,...,t)的(1.1)的等单变形导出了非线性Pfaffian方程组的完全可积系统。该系统可以被视为第六 Painlev 方程的推广。最近，K. Okamoto [3] 通过考虑以下具有 N 个变形参数 t---(tl, "’’, tN) 的 Fuchsian 型方程的等单变形，得到了哈密顿系统
(1.1) d2Y. ---p(x t)y. dx He showed that the sixth Painlev equation is just a deformation equation of a linear equation (1.1) of Fuchsian type, where t is a deformation parameter. The above result was extended by R. Garnier [2] in two directions. Firstly, he showed that the other five equations of Painlev can be obtained from the isomonodromic deformation of linear equations with irregular singular points of the form (1.1). Secondly, he derived a completely integrable system of nonlinear Pfaffian equations from the isomonodromic deformation of (1.1) with N deformation parameters t=(t,, ..., t). This system can be considered as a generalization of the sixth Painlev equation. Recently K. Okamoto [3] obtained a Hamiltonian system by considering the isomonodromic deformation of the following equation of Fuchsian type with N deformation parameters t---(tl, "’’, tN)