THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS

Nail H. Ibragimov; Aliya A. Gainetdinova

doi:10.11948/2017055

2017 Volume 7 Issue 3

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Nail H. Ibragimov, Aliya A. Gainetdinova. THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 872-883. doi: 10.11948/2017055

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Nail H. Ibragimov, Aliya A. Gainetdinova. THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 872-883. doi: 10.11948/2017055

THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS

1 Research Centre ALGA:Advances in Lie Group Analysis, Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden;
2 Laboratory "Group analysis of mathematical models in natural and engineering sciences", Ufa State Aviation Technical University, Karl Marx Str. 12, 450 000 Ufa, Russia

Abstract

Abstract

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.
- Time dependent dynamical system /
- nonlinear superposition of solutions /
- Vessiot-Guldberg-Lie algebra L₄ /
- standard forms of L₄
MSC: 34A;34A34;70G65

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References

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