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Three-dimensional dynamical systems admitting nonlinear superposition with three-dimensional Vessiot-Guldberg-Lie algebras
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
Ufa State Aviat Tech Univ, Rus.
2016 (English)In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 52, 126-131 p.Article in journal (Refereed) Published
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Abstract [en]

The recent method of integration of non-stationary dynamical systems admitting nonlinear superpositions is applied to the three-dimensional dynamical systems associated with three-dimensional Vessiot-Guldberg-Lie algebras L-3. The investigation is based on Bianchi's classification of real three-dimensional Lie algebras and realizations of these algebras in the three-dimensional space. Enumeration of the Vessiot-Guldberg-Lie algebras L-3 allows to classify three-dimensional dynamical systems admitting nonlinear superpositions into thirty one standard types by introducing canonical variables. Twenty four of them are associated with solvable Vessiot-Guldberg-Lie algebras and can be reduced to systems of first-order linear equations. The remaining seven standard types are nonlinear. Integration of the latter types is an open problem. (C) 2015 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
2016. Vol. 52, 126-131 p.
Keyword [en]
Dynamical system, Nonlinear superposition, Vessiot-Guldberg-Lie algebra
National Category
Mathematics Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-11344DOI: 10.1016/j.aml.2015.08.012ISI: 000364892900019OAI: oai:DiVA.org:bth-11344DiVA: diva2:890746
Available from: 2016-01-04 Created: 2016-01-04 Last updated: 2017-06-22Bibliographically approved

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Ibragimov, Nail

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