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The Riemann-Hilbert approach to exponentially small asymptotics in Painlevé I

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AR2W02 - Mathematics of beyond all-orders phenomena

In this talk, we revisit the calculation of exponentially small terms in the asymptotic expansion of tronquée and tritronquée solutions of the Painlevé I equation. Employing the isomonodromy approach, as proposed by Kapaev, we show how perturbative and non-perturbative asymptotic expansions can be obtained using local parametrices in terms of classical special functions.

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

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