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Regular and Chaotic Dynamics, 2017, Volume 22, Issue 3, Pages 266–271
DOI: https://doi.org/10.1134/S1560354717030066 (Mi rcd256) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

Ilia Yu. Gaiur, Nikolay A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia
Citations (2)
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DOI: https://doi.org/10.1134/S1560354717030066
Abstract: 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.
Keywords: $P_2^2$ equation, isomonodromy deformations technique, special functions, Painlevé transcendents.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.9746.2017/BCh
This work was supported by the Ministry of Education and Science of the Russian Federation (basic part of the state assignment, project no. 1.9746.2017/BCh).
Received: 14.04.2017
Accepted: 11.05.2017
Bibliographic databases:
Document Type: Article
MSC: 34E10
Language: English
Citation: Ilia Yu. Gaiur, Nikolay A. Kudryashov, “Weak Nonlinear Asymptotic Solutions for the Fourth Order Analogue of the Second Painlevé Equation”, Regul. Chaotic Dyn., 22:3 (2017), 266–271
Citation in format AMSBIB
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\by Ilia Yu. Gaiur, Nikolay A. Kudryashov
\paper Weak Nonlinear Asymptotic Solutions for the Fourth Order Analogue of the Second Painlevé Equation
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 3
\pages 266--271
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    • This publication is cited in the following 2 articles:
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