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Gaiur, Ilia Yu.; Kudryashov, Nikolay A.

Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation. (English) Zbl 1387.34124

Regul. Chaotic Dyn. 22, No. 3, 266-271 (2017).
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 \(\phi=\frac{2}{5}\,\pi (2 n + 1),\,n\in\mathbb{N}\).
Reviewer: Tsvetana Stoyanova (Sofia)

Cited in 2 Documents

MSC:

34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34M56 Isomonodromic deformations for ordinary differential equations in the complex domain

Keywords:

\(P^2_2\) equation; isomonodromy deformations technique; special functions; Painlevé transcendents
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References:

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