Projective differential geometrical structure of the Painlevé equations

DOI10.1006/jdeq.1999.3628zbMath0938.34081OpenAlexW2049786059MaRDI QIDQ1806157

Ljudmila A. Bordag, Mikhail Vasilievich Babich

Publication date: 20 December 1999

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://cds.cern.ch/record/351495

zbMATH Keywords

invariantsPainlevé equations

Mathematics Subject Classification ID

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

Related Items (19)

Equivalence classes for Emden equations ⋮ Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. I. ⋮ Open problems for Painlevé equations ⋮ Group classification of projective type second-order ordinary differential equations ⋮ On a surface isolated by Gambier ⋮ Lie point symmetries and ODEs passing the Painlevé test ⋮ Solution of the equivalence problem for the Painlevé IV equation ⋮ Generalized Bonnet surfaces and Lax pairs of PVI ⋮ Point equivalence of second-order ordinary differential equations to the fifth Painlevé equation with one and two nonzero parameters ⋮ Normal form for second order differential equations ⋮ Equivalence of ordinary differential equations \(y = R(x, y)y^{\prime 2} + 2Q(x, y)y' +P(x, y)\) ⋮ Simple zero property of some holomorphic functions on the moduli space of tori ⋮ Equivalence of second-order ordinary differential equations to Painlevé equations ⋮ Point equivalence of second-order ODEs: maximal invariant classification order ⋮ Point classification of second order ODEs and its application to Painlevé equations ⋮ Solutions of the buoyancy-drag equation with a time-dependent acceleration ⋮ Solution of the equivalence problem for the third Painlevé equation ⋮ Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant ⋮ New \(2\times 2\)-matrix linear problems for the Painlevé equations III, V

Cites Work

• The isomonodromic deformation method in the theory of Painlevé equations
• Investigation of dynamical systems using tools of the theory of invariants and projective geometry
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• RECENT PROGRESS OF GAUSS-SCHWARZ THEORY AND RELATED GEOMETRIC STRUCTURES
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