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

Resumo

The fourth-order analogue of the second Painlevé equation is considered. The monodromy manifold for a Lax pair associated with the P₂² 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 ϕ = \(\frac{2}{5}\)π(2n + 1) on the complex plane have been found by the isomonodromy deformations technique.