Geodesic
The Boutroux ansatz for the second Painleve equation in the complex domain
Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 587-609

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An asymptotic representation of the general solution of the second Painlevé equation is constructed in a sector of the complex $z$-plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of $\arg z$. Explicit expressions of these functions are given, and an approximation as $|z|\to\infty$ is proved for the initial Painlevé function outside a small neighborhood of its lattice of poles. 
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     author = {V. Yu. Novokshenov},
     title = {The {Boutroux} ansatz for the second {Painleve} equation in the complex domain},
     journal = {Izvestiya. Mathematics },
     pages = {587--609},
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     volume = {37},
     number = {3},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a6/}
}
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V. Yu. Novokshenov. The Boutroux ansatz for the second Painleve equation in the complex domain. Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 587-609. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a6/