Weakly nonlinear solutions of equationP 1 2

Using the isomonodromic deformation method, we study the equation P ₁ ² , $$\frac{1}{{10}}y^{(4)} + y''y + \frac{1}{2}(y')^2 + y^3 = x$$ , which is the first higher equation in the hierarchy of the first Painlevé equation. We construct the asymptotics of its weakly nonlinear solutions for x→∞ along the Stokes rays, and those of the real regular solutions for x→±∞. Bibliography: 11 titles.