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Zbl 1080.34071
Kapaev, A.A.
Quasi-linear Stokes phenomenon for the Painlevé first equation. (English)
[J] J. Phys. A, Math. Gen. 37, No. 46, 11149-11167 (2004). ISSN 0305-4470

Author's abstract: Using the Riemann-Hilbert approach, the Psi-function corresponding to the solution of the first Painlevé equation $y_{xx}= 6y^2+ x$ with the asymptotic behaviour $y\sim\pm \sqrt{(-x/6})$ 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.
[Chaman Lal Koul (Jaipur)]

MSC 2000:: *34M40 Stokes phenomena and connection problems
34M55 Painlevé and other special equations

Keywords: Psi-function; quasi-linear Stokes phenomenon; Riemann-Hilbert problem; asymptotics of Painlevé

Cited in: Zbl 1245.34087

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