Geodesic
Weaknonlinear solutions of the $\mathbb{P}_1^2$ equation
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 88-109 
A. A. Kapaev. Weaknonlinear solutions of the $\mathbb{P}_1^2$ equation. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 88-109. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a5/
@article{ZNSL_1991_187_a5,
     author = {A. A. Kapaev},
     title = {Weaknonlinear solutions of the $\mathbb{P}_1^2$ equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--109},
     year = {1991},
     volume = {187},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

On the base of the isomonodromy deformation method the ($\mathrm{P}_1^2$) $$ \frac1{10}y^{(4)}+y''y+\frac12(y')^2+y^3=x $$ which is the first higher equation in the hierarchy of the first Painlevé equation is studied. The asymptotics of weaknonlinear solutions for $x\to\infty$ along the Stokes rays and asymptotics of real regular solutions for real $x\to\pm\infty$ are constructed.