On the nesting of Painlevé hierarchies: a Hamiltonian approach

DOI10.1016/j.chaos.2012.03.010zbMath1264.37028OpenAlexW2041099361MaRDI QIDQ1952534

Andrew Pickering

Publication date: 31 May 2013

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2012.03.010

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) Volterra integral equations (45D05)

Related Items

Nonisospectral scattering problems and similarity reductions ⋮ On matrix Painlevé hierarchies ⋮ Solution classes of the matrix second Painlevé hierarchy ⋮ A special solution technique: further extensions ⋮ Bäcklund transformations for a new extended Painlevé hierarchy ⋮ Generalized scaling reductions and Painlevé hierarchies ⋮ The Prelle-Singer method and Painlevé hierarchies ⋮ On an extended second Painlevé hierarchy ⋮ Auto-Bäcklund transformations and special integrals for differential-delay Painlevé hierarchies

Cites Work

• Unnamed Item
• On special solutions of second and fourth Painlevé hierarchies
• On a generalized \(2+1\) dispersive water wave hierarchy
• Coalescence limits for higher order Painlevé equations
• Non-autonomous Hénon-Heiles systems
• The first and second Painlevé equations of higher order and some relations between them
• Integration via modification: a method of reduction of order for systems of ordinary differential equations
• Mathematics of dispersive water waves
• Bäcklund transformations for fourth Painlevé hierarchies
• Painlevé hierarchies and the Painlevé test
• Non-isospectral lattice hierarchies in 2 + 1 dimensions and generalized discrete Painlevé hierarchies
• A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions
• Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
• New 2+1 dimensional nonisospectral Toda lattice hierarchy
• A method of reduction of order for discrete systems
• Bäcklund transformations for a discrete second Painlevé hierarchy
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
• The discrete first, second and thirty-fourth Painlevé hierarchies
• Nonisospectral scattering problems: A key to integrable hierarchies
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Construction scheme for discrete Miura transformations
• Rational Solutions of Painlevé Equations