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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2008, Volume 5, Pages 42–50
(Mi semr90)
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Research papers
On group-theoretical properties of equation of dynamics of microsrtuctures
N. V. Lyubashevskaya Novosibirsk State University
Abstract:
We discuss group-theoretical properties of equation describing formation and evolution of defects in microstructures. Invariant solutions of equation are obtained by optimal system of subalgebras of Lie
algebra permissible by considering equation. It is shown that optimal system consists of $3$ one-dimensional subalgebras, $13$ two-dimensional subalgebras, $7$ tree-dimensional subalgebras. Each representative of optimal system generates invariant solution of rang $3$, $2$ or $1$ with corresponding number of independent variables. All factor equations describing invariant solutions of considering equation are constructed.
Received January 9, 2008, published March 10, 2008
Citation:
N. V. Lyubashevskaya, “On group-theoretical properties of equation of dynamics of microsrtuctures”, Sib. Èlektron. Mat. Izv., 5 (2008), 42–50
Linking options:
https://www.mathnet.ru/eng/semr90 https://www.mathnet.ru/eng/semr/v5/p42
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Statistics & downloads: |
Abstract page: | 181 | Full-text PDF : | 41 | References: | 40 |
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