Asymptotic expressions for the second Painleve functions

The method of isomonodromic deformations is used to investigate the asymptotic properties of solutions of the second Painleve equation. The leading terms as x → ±∞ of the second Painleve functions are constructed for the general case. The parameters of the asymptotic behavior are expressed in terms of first integrals of the Painlevel equation, which are the monodromy data of the associated system of linear ordinary differential equations with rational coefficients. The asymptotic behaviors of the real and imaginary second Painleve functions are separated