Three-dimensional dynamical systems admitting nonlinear superposition with three-dimensional Vessiot-Guldberg-Lie algebras

DOI10.1016/j.aml.2015.08.012zbMath1343.34085OpenAlexW1425585776MaRDI QIDQ901009

Aliya A. Gainetdinova, Nail H. Ibragimov

Publication date: 23 December 2015

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2015.08.012

zbMATH Keywords

dynamical systemnonlinear superpositionVessiot-Guldberg-Lie algebra

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14)

Related Items (6)

A functional realization of 𝔰𝔩(3, ℝ) providing minimal Vessiot–Guldberg–Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras ⋮ Poisson–Hopf algebra deformations of Lie–Hamilton systems ⋮ THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS ⋮ Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras ⋮ Lie symmetry analysis of the Heisenberg equation ⋮ Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra

Cites Work

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• Classification of three-dimensional Lie algebras in \(\mathbb{R}^3\) and their second-order differential invariants
• Canonical forms for systems of two second-order ordinary differential equations
• Realizations of real low-dimensional Lie algebras

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