All Binomial‐Type Painlevé Equations of the Second Order and Degree Three or Higher

DOI10.1002/sapm1993902119zbMath0807.34007OpenAlexW2198179308MaRDI QIDQ4286876

Christopher M. Cosgrove

Publication date: 12 April 1994

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1993902119

zbMATH Keywords

Painlevé propertyPainlevé transcendentselliptic functionsquadratures

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

A perturbative Painlevé approach to nonlinear differential equations ⋮ Second-order second-degree Painlevé equations related with Painlevé I–VI equations and Fuchsian-type transformations ⋮ Open problems for Painlevé equations ⋮ Lie point symmetries and ODEs passing the Painlevé test ⋮ Binomial‐Type Ordinary Differential Equations of the Third Order ⋮ Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1 ⋮ Painlevé Classification of Binomial Type Ordinary Differential Equations of the Arbitrary Order ⋮ Do all integrable equations satisfy integrability criteria? ⋮ On a system of two linear-fractional differential equations of order \(n\) with the Painlevé property ⋮ Third order differential equations with fixed critical points ⋮ On the discrete form of the Fokas--Ablowitz equation ⋮ Bäcklund transformations for higher order Painlevé equations ⋮ Some properties of the Nesterenko differential sequence

Cites Work

• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points
• Equations différentielles du second ordre en Y et du second degré en Y dont l'intégrale générale est à points critiques fixes
• Differential equations with fixed critical points. II
• Differential equations with fixed critical points
• The Painlevé property for partial differential equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability
• Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree
• Painlevé Classification of All Semi linear Partial Differential Equations of the Second Order. I. Hyperbolic Equations in Two Independent Variables
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Painlevé Classification of All Semilinear Partial Differential Equations of the Second Order. II. Parabolic and Higher Dimensional Equations

This page was built for publication: All Binomial‐Type Painlevé Equations of the Second Order and Degree Three or Higher