Geodesic
On group-theoretical properties of equation of dynamics of microsrtuctures
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 42-50

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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. 
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     author = {N. V. Lyubashevskaya},
     title = {On group-theoretical properties of equation of dynamics of microsrtuctures},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {42--50},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a5/}
}
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N. V. Lyubashevskaya. On group-theoretical properties of equation of dynamics of microsrtuctures. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 42-50. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a5/