Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation
type: Item
instance of: scholarly article
title: Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation
zbMATH Open document ID: 1387.34124
DOI: 10.1134/S1560354717030066
author: Ilia Yu. Gaiur
author: Nikolai A. Kudryashov
published in: Regular and Chaotic Dynamics
publication date: 2018-02-06T00:00:00Z
review text: 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 \(\phi=\frac{2}{5}\,\pi (2 n + 1),\,n\in\mathbb{N}\).
reviewed by: Tsvetana Stoyanova
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34M56
zbMATH DE Number: 6835230
zbMATH Keywords: \(P^2_2\) equation
zbMATH Keywords: isomonodromy deformations technique
zbMATH Keywords: special functions
zbMATH Keywords: Painlevé transcendents
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6835230