Nonlinear differential equations associated with the second Painlevé equation are considered. Transformations for solutions of the singular manifold equation are presented. It is shown that rational solutions of the singular manifold equation are determined by means of the Yablonskii-Vorob’ev polynomials. It is demonstrated that rational solutions for some differential equations are also expressed via the Yablonskii-Vorob’ev polynomials.

中文翻译：

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与第二个Painlevé方程有关的方程的有理解

考虑与第二个Painlevé方程关联的非线性微分方程。提出了奇异流形方程解的变换。结果表明，利用Yablonskii-Vorob'ev多项式确定了奇异流形方程的有理解。证明了一些微分方程的有理解也通过Yablonskii-Vorob'ev多项式表示。