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Integration of dynamical systems admitting nonlinear superposition
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
2016 (English)In: JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS, ISSN 2330-152X, Vol. 4, no 2, 91-106 p.Article, review/survey (Refereed) Published
Abstract [en]

A method of integration of non-stationary dynamical systems admitting nonlinear superpositions is presented. The method does not require knowledge of symmetries of the differential equations under consideration. The integration procedure is based on classification of Vessiot-Guldberg-Lie algebras associated with nonlinear superpositions. It is shown that the systems associated with one-and two-dimensional Lie algebras can be integrated by quadrature upon introducing Lie's canonical variables. It is not necessary to know symmetries of a system in question in this approach. Two-dimensional non-stationary dynamical systems with three-dimensional Vessiot-Guldberg-Lie algebras are classified into thirteen standard forms. Ten of them are integrable by quadrature. The remaining three standard forms lead to the Riccati equations. Integration of perturbed dynamical systems possessing approximate nonlinear superposition is discussed.

Place, publisher, year, edition, pages
American Scientific Publishers, 2016. Vol. 4, no 2, 91-106 p.
Keyword [en]
Dynamical Systems, Nonlinear Superposition, Vessiot-Guldberg-Lie Algebra, Semi-Separable Systems, Integration Method, Perturbed Dynamical Systems, Approximate Nonlinear Superposition
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-13621DOI: 10.1166/jcsmd.2016.1098ISI: 000388585400001OAI: oai:DiVA.org:bth-13621DiVA: diva2:1057204
Available from: 2016-12-16 Created: 2016-12-16 Last updated: 2016-12-19Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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Output format
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  • asciidoc
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