The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy

DOI10.1016/j.chaos.2006.07.032zbMath1132.33339arXivnlin/0605018OpenAlexW2045698124MaRDI QIDQ2482400

Maria V. Demina, Nikolay A. Kudryashov

Publication date: 16 April 2008

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0605018

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17)

Related Items

Invariant algebraic curves for Liénard dynamical systems revisited ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Soliton, rational and special solutions of the Korteweg-de Vries hierarchy ⋮ Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies ⋮ Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation ⋮ Special polynomials associated with some hierarchies ⋮ Liouvillian integrability of the generalized Duffing oscillators ⋮ Special polynomials and rational solutions of the hierarchy of the second Painlevé equation ⋮ Special polynomials associated with rational solutions of some hierarchies ⋮ Relations between zeros of special polynomials associated with the Painlevé equations ⋮ The generalized Yablonskii-Vorob'ev polynomials and their properties ⋮ Puiseux integrability of differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Power expansions for solution of the fourth-order analog to the first Painlevé equation
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Remarks on the Yablonskii-Vorob'ev polynomials
• On coefficients of Yablonskii-Vorob'ev polynomials
• Umemura polynomials for the Painlevé V equation
• On the Umemura polynomials for the Painlevé III equation
• Non-autonomous Hénon-Heiles systems
• The first and second Painlevé equations of higher order and some relations between them
• Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation
• Rational solutions for Schwarzian integrable hierarchies
• Solutions of the second and fourth Painlevé equations, I
• The second Painlev  equation, its hierarchy and associated special polynomials
• The third Painlev  equation and associated special polynomials
• Remarks on the Yablonskii-Vorob’ev polynomials
• Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation