Quasi-linear Stokes phenomenon for the second Painlevé transcendent

Abstract

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

19 pages, LaTeX

References in corpus (1)

• A priori $L^p$ estimates for solutions of Riemann-Hilbert Problems

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