Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation (Q1695055)

The authors consider the \(P^2_2\) equation \[ \, y_{xxxx} - 10 y^2\,y_{xx} - 10 y\,y^2_x + 6 y^5 -y\,x +\alpha=0 \, \] with \(x\in\mathbb{C}\). Using the isomonodromy deformations technique they construct asymptotic solutions of the \(P^2_2\) equation on the complex plane. These solutions are expressed in terms of the trigonometric functions in Boutroux variables along the rays \(\phi=\frac{2}{5}\,\pi (2 n + 1),\,n\in\mathbb{N}\).