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

الأصل · EN

Using the Riemann-Hilbert approach, we explicitly construct the asymptotic Ψ-function corresponding to the solution y ±√-x/2 as |x|→∞ to the second Painlevé equation yxx=2y³+xy-α. We precisely describe the exponentially small jump in the dominant solution and the coefficient asymptotics in its power-like expansion.