Geodesic
On symmetrical solutions for the first and second Painlev\'e equations
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 129-138

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Asymptotics for the initial value problems for symmetrical solutions of $\mathbb{P}_1$ and $\mathbb{P}_2$ equations are obtained, i.e. the connection formulae for parameters which describe the behaviour of these solutions near zero and infinity are given. 
@article{ZNSL_1991_187_a7,
     author = {A. V. Kitaev},
     title = {On symmetrical solutions for the first and second {Painlev\'e} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--138},
     publisher = {mathdoc},
     volume = {187},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a7/}
}
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A. V. Kitaev. On symmetrical solutions for the first and second Painlev\'e equations. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 129-138. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a7/