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Integration of dynamical systems admitting nonlinear superposition
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
2016 (engelsk)Inngår i: JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS, ISSN 2330-152X, Vol. 4, nr 2, s. 91-106Artikkel, forskningsoversikt (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
American Scientific Publishers, 2016. Vol. 4, nr 2, s. 91-106
Emneord [en]
Dynamical Systems, Nonlinear Superposition, Vessiot-Guldberg-Lie Algebra, Semi-Separable Systems, Integration Method, Perturbed Dynamical Systems, Approximate Nonlinear Superposition
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Identifikatorer
URN: urn:nbn:se:bth-13621DOI: 10.1166/jcsmd.2016.1098ISI: 000388585400001OAI: oai:DiVA.org:bth-13621DiVA, id: diva2:1057204
Tilgjengelig fra: 2016-12-16 Laget: 2016-12-16 Sist oppdatert: 2016-12-19bibliografisk kontrollert

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