Weaknonlinear solutions of the $\mathbb{P}_1^2$ equation

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.