Quasi-linear Stokes phenomenon for the Painlevé first equation

Abstract

Using the Riemann-Hilbert approach, the $\Psi$-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.

version accepted for publication

References in corpus (4)

• Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime
• Quasi-linear Stokes phenomenon for the second Painlevé transcendent
• Monodromy approach to the scaling limits in the isomonodromy systems
• Monodromy deformation approach to the scaling limit of the Painleve first equation

Cited by in corpus (34)

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