# Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent

Presented by:
A Kapaev [Steklov]
Date:
Monday 5th November 2001 - 15:00 to 16:00
Venue:
INI Seminar Room 1
Abstract:
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlev\'e 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 asymptotics of the coefficients is found.