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

Published 9 Feb 2022 in math-ph, math.CA, math.MP, and nlin.SI | (2202.04217v1)

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.

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