A Lie systems approach to the Riccati hierarchy and partial differential equations

DOI10.1016/j.jde.2017.02.038zbMath1436.34031arXiv1612.00256OpenAlexW2560269824MaRDI QIDQ525968

Javier de Lucas, A. Michel Grundland

Publication date: 8 May 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.00256

zbMATH Keywords

Lie systemconformal Lie algebra of vector fieldsGambier equationsprojective Lie algebra of vector fieldsprojective Riccati equationRiccati hierarchy

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14)

Related Items (7)

Multisymplectic structures and invariant tensors for Lie systems ⋮ Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit ⋮ Lie–Hamilton systems on curved spaces: a geometrical approach ⋮ Geometry-preserving numerical methods for physical systems with finite-dimensional Lie algebras ⋮ Recent advances on Lie systems and their applications ⋮ Geometric features of Vessiot–Guldberg Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$ ⋮ On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications

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