Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation

Abstract

Using the Riemann-Hilbert approach, we explicitly construct the asymptotic $\Psi$-function corresponding to the solution $y\sim \pm \sqrt{-x/2}$ as $|x|\to \infty$ to the second Painlevé equation $y_{xx}=2y^3+xy-\alpha$. We precisely describe the exponentially small jump in the dominant solution and the coefficient asymptotics in its power-like expansion.

arXiv commentLaTeX2e, 22 pages

References in corpus (2)

• Level-Spacing Distributions and the Airy Kernel
• Quasi-linear Stokes phenomenon for the second Painlevé transcendent

Cited by in corpus (4)

• Asymptotics for a special solution of the thirty fourth Painleve equation
• Multi-critical unitary random matrix ensembles and the general Painleve II equation
• On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation
• Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendent