Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List

DOI10.20537/nd200408zbMath1464.34007OpenAlexW3119364907MaRDI QIDQ5853583

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Publication date: 11 March 2021

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/nd734

zbMATH Keywords

Lax representationfirst integralsLiénard-type equationsPainlevé-Gambier equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Nonautonomous smooth dynamical systems (37C60)

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Cites Work

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• Completely integrable systems, Euclidean Lie algebras, and curves
• Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
• Two hierarchies of ordinary differential equations and their properties
• On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type
• Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• Linearizing Flows and a Cohomological Interpretation of Lax Equations
• Rational solutions for Schwarzian integrable hierarchies
• Separability and Lax pairs for Hénon–Heiles system
• Transcendents defined by nonlinear fourth-order ordinary differential equations

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