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

DOI10.1134/S1560354717030066zbMath1387.34124MaRDI QIDQ1695055

Ilia Yu. Gaiur, Nikolay A. Kudryashov

Publication date: 6 February 2018

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

Painlevé transcendentsspecial functions\(P^2_2\) equationisomonodromy deformations technique

Mathematics Subject Classification ID

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

Related Items (2)

Lax pairs and special polynomials associated with self-similar reductions of Sawada -- Kotera and Kupershmidt equations ⋮ Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies

Cites Work

• Power geometry and elliptic expansions of solutions to the Painlevé equations
• Special polynomials associated with the fourth order analogue to the Painlevé equations
• Two hierarchies of ordinary differential equations and their properties
• Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation
• The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy
• "ISOMONODROMY" SOLUTIONS OF EQUATIONS OF ZERO CURVATURE
• Rational solutions for Schwarzian integrable hierarchies
• THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN
• Symmetrization in the geometric theory of functions of a complex variable

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