Special polynomials associated with rational solutions of some hierarchies

DOI10.1016/j.chaos.2007.06.008zbMath1197.35235OpenAlexW2118680351MaRDI QIDQ712033

Nikolay A. Kudryashov

Publication date: 28 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2007.06.008

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Series solutions to PDEs (35C10)

Related Items (2)

Generalized Hermite polynomials for the Burgers hierarchy and point vortices ⋮ Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies

Cites Work

• Unnamed Item
• Special polynomials associated with the fourth order analogue to the Painlevé equations
• Power expansions for solution of the fourth-order analog to the first Painlevé equation
• Double Bäcklund transformations and special integrals for the \(K_{II}\) hierarchy
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Remarks on the Yablonskii-Vorob'ev polynomials
• Two hierarchies of ordinary differential equations and their properties
• 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
• On fourth-order nonlinear differential equations with the Painlevé property
• The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1
• On classes of integrable systems and the Painlevé property
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• A new hierarchy of Korteweg–de Vries equations
• Transcendents defined by nonlinear fourth-order ordinary differential equations
• 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

This page was built for publication: Special polynomials associated with rational solutions of some hierarchies