This article is cited in 3 papers

Systems of linear differential equations with non-$x$-autonomous basic Lie algebra

Yu. A. Chirkunov<sup>ab

a</sup> Novosibirsk State Technical University, Novosibirsk, RUSSIA
^b Institute of Computational Technologies SB RAS, Novosibirsk, RUSSIA

Abstract: We obtain some necessary and sufficient conditions for the non-$x$-autonomy of the basic Lie algebra of a system of first-order linear differential equations with constant coefficients over the field of complex numbers. Using these results, we establish the $x$-autonomy of the basic Lie algebra of some systems of equations of mathematical physics.

Keywords: $x$-autonomy of the basic Lie algebra, canonical systems of linear differential equations, criteria of $x$-autonomy.

UDC: 517.956

Received: 23.07.2009

 English version: Journal of Applied and Industrial Mathematics, 2012, 6:1, 31–41

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