Coalescence limits for higher order Painlevé equations

DOI10.1016/S0375-9601(02)00972-6zbMath0997.34084OpenAlexW2168517503MaRDI QIDQ1612839

Andrew Pickering

Publication date: 4 September 2002

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(02)00972-6

zbMATH Keywords

transcendental functions

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (19)

Nonisospectral scattering problems and similarity reductions ⋮ On matrix Painlevé hierarchies ⋮ Solution classes of the matrix second Painlevé hierarchy ⋮ Lax pairs and special polynomials associated with self-similar reductions of Sawada -- Kotera and Kupershmidt equations ⋮ Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies ⋮ Rational solutions of equations associated with the second Painlevé equation ⋮ Integrability properties of a generalized reduction of the KdV6 equation ⋮ A new derivation of Painlevé hierarchies ⋮ Bäcklund transformations for a new extended Painlevé hierarchy ⋮ On the nesting of Painlevé hierarchies: a Hamiltonian approach ⋮ Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1 ⋮ On matrix fourth Painlevé hierarchies ⋮ Rational and special solutions for some Painlevé hierarchies ⋮ Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation ⋮ Bäcklund transformations for higher order Painlevé equations ⋮ On an extended second Painlevé hierarchy ⋮ Lax pairs for one of hierarchies similar to the first Painlevé hierarchy ⋮ Relations between zeros of special polynomials associated with the Painlevé equations ⋮ Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies

Cites Work

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• On a generalized \(2+1\) dispersive water wave hierarchy
• A note on the transcendency of Painlevé’s first transcendent
• Second proof of the irreducibility of the first differential equation of painlevé
• On a new non-isospectral variant of the Boussinesq hierarchy
• Nonisospectral scattering problems: A key to integrable hierarchies
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Rational Solutions of Painlevé Equations
• Confluence processes in defining manifolds for Painlevé systems

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