Quasi-linear Stokes phenomenon for the Painleve first equation

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 behaviour y similar to +/-root-x/6 as \x\ --> infinity is constructed. The exponentially small jump in the dominant solution and the coefficient asymptotics in the power-like expansion to the latter are found.