Second-order second-degree Painlevé equations related with Painlevé I–VI equations and Fuchsian-type transformations

DOI10.1063/1.532909zbMath0980.34085OpenAlexW2071157197MaRDI QIDQ4270368

Ayman Hashem Sakka, Uğurhan Muğan

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532909

zbMATH Keywords

Riccati equationstransformationsmovable branch points

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items

Painlevé Test and Higher Order Differential Equations ⋮ Second-degree Painlevé equations and their contiguity relations ⋮ Third order differential equations with fixed critical points ⋮ New Bäcklund transformations for the third and fourth Painlevé equations to equations of second order and higher degree ⋮ Bäcklund transformations for higher order Painlevé equations ⋮ New integrable equations of fourth order and higher degree related to Cosgrove’s equation ⋮ Bäcklund transformations for the second member of the first Painlevé hierarchy

Cites Work

• 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
• On the solvability of Painlevé II and IV
• On the solvability of Painleve I, III and V
• Schlesinger transformations of Painlevé II-V
• Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree
• Second-order second-degree Painlevé equations related to Painlevé IV,V,VI equations
• Second-order second degree Painlevé equations related with Painlevé I, II, III equations
• All Binomial‐Type Painlevé Equations of the Second Order and Degree Three or Higher
• On the solvability of the Painleve VI equation
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Schlesinger transformations for Painlevé VI equation