Abstract:
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=25π(2n+1) on the complex plane have been found by the isomonodromy deformations technique.
Keywords:P22 equation, isomonodromy deformations technique, special functions, Painlevé transcendents.
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).
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
\Bibitem{GaiKud17}
\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
\mathnet{http://mi.mathnet.ru/rcd256}
\crossref{https://doi.org/10.1134/S1560354717030066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3658425}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000402746300006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020190050}
Linking options:
https://www.mathnet.ru/eng/rcd256
https://www.mathnet.ru/eng/rcd/v22/i3/p266
This publication is cited in the following 2 articles:
Nikolay A. Kudryashov, “Lax Pairs and Rational Solutions of Similarity Reductions for
Kupershmidt and Sawada – Kotera Hierarchies”, Regul. Chaotic Dyn., 26:3 (2021), 271–292
Nikolay A. Kudryashov, “Lax Pairs and Special Polynomials Associated with Self-similar Reductions of Sawada – Kotera and Kupershmidt Equations”, Regul. Chaotic Dyn., 25:1 (2020), 59–77
Citation in format AMSBIB
Contact us: