On the algebraic solutions of the Painleve-III (D7) equation

Abstract

The D7 degeneration of the Painleve-III equation has solutions that are rational functions of $x^{1/3}$ for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert representation of these solutions. We demonstrate the utility of this representation by analyzing rigorously the behavior of the solutions in the large parameter limit.

35 pages, 7 figures

References in corpus (1)

• Large-degree asymptotics of rational Painleve-II functions. II

Cited by in corpus (1)

• Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III $({\mathrm{D}}_7)$ Equation