A quasi-Lie schemes approach to second-order Gambier equations

DOI10.3842/SIGMA.2013.026zbMath1279.34015arXiv1303.3434MaRDI QIDQ352494

Partha Guha, Javier de Lucas, José F. Cariñena

Publication date: 4 July 2013

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3434

zbMATH Keywords

Kummer-Schwarz equationLie systemsMilne-Pinney equationquasi-Lie schemessecond-order Gambier equationsecond-order Riccati equationsuperposition rules

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Geometric methods in ordinary differential equations (34A26) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (7)

Lie point symmetries classification of the mixed Liénard-type equation ⋮ Lie point symmetry analysis of a second order differential equation with singularity ⋮ Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit ⋮ Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of Ermakov-Pinney Lie algebra ⋮ Folding transformations of equations from the Gambier family ⋮ Nonlinear superposition formulas for two classes of non-holonomic systems ⋮ Quasi-Lie families, schemes, invariants and their applications to Abel equations

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