Rational Solutions of Equations Associated with the Second Painlevé Equation

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.