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Three-dimensional dynamical systems with four-dimensional vessiot-guldberg-lie algebras
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
Ufimskij Gosudarstvennyj Aviacionnyj Tehniceskij Universitet, RUS.
2017 (English)In: The Journal of Applied Analysis and Computation, ISSN 2156-907X, E-ISSN 2158-5644, Vol. 7, no 3, 872-883 p.Article in journal (Refereed) Published
Abstract [en]

- Dynamical systems attract much attention due to their wide applications. Many significant results have been obtained in this field from various points of view. The present paper is devoted to an algebraic method of integration of three-dimensional nonlinear time dependent dynamical systems admitting nonlinear superposition with four-dimensional Vessiot-Guldberg-Lie algebras L4. The invariance of the relation between a dynamical system admitting nonlinear superposition and its Vessiot-Guldberg-Lie algebra is the core of the integration method. It allows to simplify the dynamical systems in question by reducing them to standard forms. We reduce the three-dimensional dynamical systems with four-dimensional Vessiot-Guldberg-Lie algebras to 98 standard types and show that 86 of them are integrable by quadratures.

Place, publisher, year, edition, pages
Wilmington Scientific Publisher , 2017. Vol. 7, no 3, 872-883 p.
Keyword [en]
Nonlinear superposition of solutions, Standard forms of L4, Time dependent dynamical system, Vessiot-guldberg-lie algebra L4
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-14676DOI: 10.11948/2017055OAI: oai:DiVA.org:bth-14676DiVA: diva2:1113951
Available from: 2017-06-22 Created: 2017-06-22 Last updated: 2017-06-22

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