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Quasi-linear Stokes phenomenon for the Painlevé first equation

Andrei A. Kapaev
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Abstract

Using the Riemann-Hilbert approach, the $Ψ$-function corresponding to the solution of the first Painleve equation, $y_{xx}=6y^2+x$, with the asymptotic behavior $y\sim\pm\sqrt{-x/6}$ as $|x|\to\infty$ is constructed. The exponentially small jump in the dominant solution and the coefficient asymptotics in the power-like expansion to the latter are found.

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Andrei A. Kapaev. 2004-11-03. Quasi-linear Stokes phenomenon for the Painlevé first equation. https://doi.org/10.1088/0305-4470%2F37%2F46%2F005

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