Folding transformations of equations from the Gambier family

DOI10.1016/j.cnsns.2014.09.021zbMath1337.34018OpenAlexW1988012583MaRDI QIDQ907665

Partha Guha, Anindya Ghose Choudhury

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.09.021

zbMATH Keywords

folding transformationGambier equationAbel sequence of differential equations

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34)

Related Items (1)

Symmetries and reductions of order for certain nonlinear third- and second-order differential equations with arbitrary nonlinearity

Cites Work

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• A quasi-Lie schemes approach to second-order Gambier equations
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• Quadratic transformations for the sixth Painlevé equation
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• The Gambier mapping, revisited
• Folding transformations of the Painlevé equations
• The Gambier mapping
• Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
• Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
• Quadratic relations in continuous and discrete Painlevé equations
• Contiguity relations for linearisable systems of Gambier type
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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