University of Cambridge > > Isaac Newton Institute Seminar Series > On the Algebraic Solutions of the Painlev\'e-III (D$_7$) Equation

On the Algebraic Solutions of the Painlev\'e-III (D$_7$) Equation

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ARA2 - Applicable resurgent asymptotics: towards a universal theory

The D$_7$ degeneration of the Painlev\’e-III equation has, for certain integral parameter values, a unique algebraic solution that is a rational function of the cube root of the independent variable.  This talk will describe some properties of these solutions, develop a Riemann-Hilbert representation of them using the isomonodromy method, and explain how asymptotic properties of the solutions, including an approximation by Weierstra\ss\ elliptic functions, are obtained from that representation.  This is joint work with Robert Buckingham.

This talk is part of the Isaac Newton Institute Seminar Series series.

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