The Weiss–Tabor–Carnevale Painlevé test and Burgers’ hierarchy

DOI10.1063/1.530615zbMath0811.35130OpenAlexW2013093316MaRDI QIDQ4298594

Andrew Pickering

Publication date: 8 August 1994

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

Full work available at URL: https://doi.org/10.1063/1.530615

zbMATH Keywords

Bäcklund transformationPainlevé testBurger's equation

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

The singular manifold method revisited ⋮ Integrable hierarchies: Painlevé indices and compatibility conditions ⋮ A new derivation of Painlevé hierarchies ⋮ Generalized scaling reductions and Painlevé hierarchies ⋮ Burgers and Kadomtsev-Petviashvili hierarchies: a functional representation approach ⋮ Inverse variational problem and canonical structure of Burgers equations ⋮ A Bäcklund transformation for the Burgers hierarchy ⋮ The development of the concept of Painlevé chains for the classification of integrable higher-order differential equations ⋮ Auto-Bäcklund transformations for a matrix partial differential equation ⋮ Painlevé Tests, Singularity Structure and Integrability

Cites Work

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• A perturbative Painlevé approach to nonlinear differential equations
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• The Painlevé property for partial differential equations
• Systematics of strongly self-dominant higher-order differential equations based on the Painlevé analysis of their singularities
• Application of hereditary symmetries to nonlinear evolution equations
• Evolution equations possessing infinitely many symmetries
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• The partial differential equation u_t + uu_x = μ_xx