Variations for some Painlevé equations

DOI10.3842/SIGMA.2019.088zbMath1429.33034arXiv1705.07625MaRDI QIDQ2280427

Primitivo Belén Acosta-Humánez, Jaap Top, Marius van der Put

Publication date: 18 December 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07625

zbMATH Keywords

Hamiltonian systemsvariational equationsPainlevé equationsdifferential Galois groups

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17)

Related Items

Classical solutions of the degenerate fifth Painlevé equation ⋮ Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On algebraic relations between solutions of a generic Painlevé equation
• Non-integrability of some Painlevé VI-equations and dilogarithms
• Moduli spaces for linear differential equations and the Painlevé equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• First order algebraic differential equations. A differential algebraic approach
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• Galoisian methods for testing irreducibility of order two nonlinear differential equations
• Special polynomials associated with rational solutions of the fifth Painlevé equation
• Painlevé differential equations in the complex plane
• Painlevé equations, elliptic integrals and elementary functions
• Equivalence of differential equations of order one
• Order one equations with the Painlevé property
• Isomonodromy for the degenerate fifth Painlevé equation
• Non-Integrability of Painlevé V Equations in the Liouville Sense and Stokes Phenomenon
• Birational automorphism groups and differential equations
• Non-integrability of Painlevé VI equations in the Liouville sense
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• Non-integrability of the second Painleve equation as a Hamiltonian system
• Nonautonomous Hamiltonian Systems and Morales–Ramis Theory I. The Case $\ddot{x}=f(x,t)$
• Second proof of the irreducibility of the first differential equation of painlevé
• Solutions of the second and fourth Painlevé equations, I
• R. Fuchs’ problem of the Painlevé equations from the first to the fifth
• Non-integrability of the fourth Painlevé equation in the Liouville–Arnold sense