INVARIANT SYSTEMS OF THREE SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH A SIX-DIMENSIONAL LIE ALGEBRA

Author(s):  V.O. Lukashchuk, candidate of Sciences, associate Professor, Ufa State Aviation Technical University, Ufa, Russia, voluks@gmail.com

K.R. Kadyrova, Ufa State Aviation Technical University, Ufa, Russia

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  We consider a six-dimensional Lie algebra with two nonzero commutation relations. We proved that there are 21 types of such non-similar Lie algebras in the space of first-order differential operators on a space of four variables. Then we construct canonical forms of basis operators for the realizations in the space of four variables of these types of non-similar Lie algebras. The number of second-order differential invariants and additional invariant relations was calculated for each basis operators. The general forms of the corresponding invariant systems of three second-order ordinary differential equations are obtained for fifteen non-similar Lie algebras. An illustrative example is given to show how the results can be used for integration of a system of three second-order ordinary differential equations admitting considered six-dimensional Lie algebra.

Keywords:  Lie algebra, differential invariants, invariant system of ordinary differential equations

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