On a unified approach to transformations and elementary solutions of Painlevé equations
On a unified approach to transformations and elementary solutions of Painlevé equations
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关于 Painlevé 方程变换和初等解的统一方法
DOI：
10.1063/1.525260
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发表时间：
1982
影响因子：
1.3
通讯作者：
M. Ablowitz
中科院分区：
文献类型：
--
作者：
A. Fokas;M. Ablowitz
给出了一种研究Painleve型二阶方程变换性质的算法方法.这种方法，它利用这些方程的奇异结构，产生明确的转换，涉及的解决方案的Painleve方程II-VI，不同的参数。这些变换很容易生成方程的有理解和其他初等解。本文还讨论了Painleve方程与某些新的Painleve型二阶导数二次方程之间的关系。
An algorithmic method is developed for investigating the transformation properties of second‐order equations of Painleve type. This method, which utilizes the singularity structure of these equations, yields explicit transformations which relate solutions of the Painleve equations II–VI, with different parameters. These transformations easily generate rational and other elementary solutions of the equations. The relationship between Painleve equations and certain new equations quadratic in the second derivative of Painleve type is also discussed.