THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN

Abstract

An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.