Bäcklund transformations for a discrete second Painlevé hierarchy

DOI10.1063/1.3041621zbMath1200.39007OpenAlexW2087808363MaRDI QIDQ3650880

Andrew Pickering

Publication date: 7 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3041621

zbMATH Keywords

differential equationslattice theory

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Difference equations (39A99) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (16)

On matrix Painlevé hierarchies ⋮ Solution classes of the matrix second Painlevé hierarchy ⋮ Bäcklund transformations for a matrix second Painlevé equation ⋮ A new kind of Bäcklund transformation for partial differential equations ⋮ Integrability properties of a generalized reduction of the KdV6 equation ⋮ Exact solutions of a novel integrable partial differential equation ⋮ On the nesting of Painlevé hierarchies: a Hamiltonian approach ⋮ On matrix fourth Painlevé hierarchies ⋮ Auto-Bäcklund transformations for a differential-delay equation ⋮ A method of reduction of order for discrete systems ⋮ On an extended second Painlevé hierarchy ⋮ Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation ⋮ Auto-Bäcklund transformations for a matrix partial differential equation ⋮ Bäcklund transformations for new fourth Painlevé hierarchies ⋮ Auto-Bäcklund transformations and special integrals for differential-delay Painlevé hierarchies ⋮ Auto-Bäcklund transformations and integrability of ordinary and partial differential equations

Cites Work

• Unnamed Item
• Bäcklund transformations for discrete Painlevé equations: discrete P\(_{\text{II}}\)-P\(_{\text{V}}\)
• Schlesinger transformations for discrete second Painlevé equation: d-\(P_{II}\)
• Bäcklund transformations for fourth Painlevé hierarchies
• Non-isospectral lattice hierarchies in 2 + 1 dimensions and generalized discrete Painlevé hierarchies
• A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions
• The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painlevé hierarchy
• Miura transforms for discrete Painleve equations
• The discrete first, second and thirty-fourth Painlevé hierarchies
• Construction scheme for discrete Miura transformations
• Rational Solutions of Painlevé Equations

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