# Weak Nonlinear Asymptotic Solutions for the Fourth Order Analogue of the Second Painlevé Equation

*2017, Volume 22, Number 3, pp. 266-271*

Author(s):

**Kudryashov N. A., Gaur I. Y.**

The fourth-order analogue of the second Painlevé equation is considered. The monodromy manifold for a Lax pair associated with the $P_2^2$ equation is constructed. The direct monodromy problem for the Lax pair is solved. Asymptotic solutions expressed via trigonometric functions in the Boutroux variables along the rays $\phi = \frac{2}{5}\pi(2n+1)$ on the complex plane have been found by the isomonodromy deformations technique.

Access to the full text on the Springer website |