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Quasi-linear Stokes phenomenon for the second Painlevé transcendent

A. R. Its·A. A. Kapaev
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Abstract

Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlevé equation $y_{xx}=2y^3+xy-α$. The precise description of the exponentially small jump in the dominant solution approaching $α/x$ as $|x|\to\infty$ is given. For the asymptotic power expansion of the dominant solution, the coefficient asymptotics is found.

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A. R. Its, A. A. Kapaev. 2001-08-07. Quasi-linear Stokes phenomenon for the second Painlevé transcendent. https://doi.org/10.1088/0951-7715%2F16%2F1%2F321

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