Folding transformations of equations from the Gambier family
type: Item
instance of: scholarly article
title: Folding transformations of equations from the Gambier family
zbMATH Open document ID: 1337.34018
author: Partha Guha
author: A. Ghose Choudhury
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2016-01-26T00:00:00Z
review text: The authors investigate the connection between the Gambier equation (a second-order differential equation with cubic polynomial) and the Abel chain of equations which is a generalization of the Riccati chain (for quadratic nonlinearities). For this, they study the first and second integrals of the Gambier equation and use a generalized folding transformation.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 6535620
zbMATH Keywords: Gambier equation
zbMATH Keywords: Abel sequence of differential equations
zbMATH Keywords: folding transformation
reviewed by: Smail Djebali
MaRDI profile type: Publication
full work available at URL: j.cnsns.2014.09.021
OpenAlex ID: W1988012583
cites work: A quasi-Lie schemes approach to second-order Gambier equations
cites work: Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
cites work: The Gambier mapping
cites work: The Gambier mapping, revisited
cites work: Contiguity relations for linearisable systems of Gambier type
cites work: Q3692073
cites work: Dynamical studies of equations from the Gambier family
cites work: Q3292729
cites work: Q5843703
cites work: Quadratic transformations for the sixth Painlevé equation
cites work: Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
cites work: Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
cites work: The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0
cites work: Quadratic relations in continuous and discrete Painlevé equations
cites work: Folding transformations of the Painlevé equations
DOI: 10.1016/J.CNSNS.2014.09.021
description: scientific article; zbMATH DE number 6535620