Connection Results for the First Painlevé Equation
Connection Results for the First Painlevé Equation
复制标题
第一个 Painlevé 方程的连接结果
DOI：
10.1007/978-1-4899-1158-2_4
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
M. Kruskal
中科院分区：
文献类型：
--
作者：
N. Joshi;M. Kruskal
第一个Painlevé方程(PI)的关联问题是将Painlevé方程在一条射线上的解在自变量的复平面上的渐近行为与它在另一条射线上的可能行为联系起来。连接结果，即与指定这种渐近行为的参数相关的公式，在物理应用中是有意义的，特别是在统计力学和弦理论中。本文对一般(四实参数)椭圆函数型渐近性态和特殊(两实参数)近乎无穷远扇区无极点的PI型渐近性态，给出了新的联系结果。
The connection problem for the first Painlevé equation (PI) is to relate the asymptotic behavior of a solution of PIvalid on a ray approaching infinity, in the complex plane of the independent variable, to its possible behaviors on another such ray. Connection results, the formulæ relating the parameters which specify such asymptotic behaviors, are of interest in physical applications, in particular, in statistical mechanics and string theory. New connection results for PIare announced in this paper, both for generic (four-real-parameter) elliptic-function-type asymptotic behaviors and special (two-real-parameter) behaviors that are free of poles in certain sectors near infinity.