Geodesic
Exact solutions to the equations of the dynamic asymmetric model of elasticity
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 38-50

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Using the group stratification of the equations of the dynamic asymmetric model of elasticity effectively used in the study of elastic materials made of polymers, we obtain a system that, after renaming the functions, becomes equivalent to these equations and contains fewer additional functions than the union of the resolving and automorphic systems of the accomplished group stratification. Among first-order systems equivalent to these equations it contains the least number of additional functions and is the only such system up to a nondegenerate linear transformation of the additional functions. We find its principal Lie transformation group, an optimal system of its subgroups, and their universal invariants. Some invariant and partially invariant exact solutions are found; their physical meaning is explained.
Keywords: asymmetric elasticity, optimal system of subgroups
Mots-clés : group stratification, invariant solutions. 
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     title = {Exact solutions to the equations of the dynamic asymmetric model of elasticity},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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N. F. Belmetsev; Yu. A. Chirkunov. Exact solutions to the equations of the dynamic asymmetric model of elasticity. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 38-50. http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a3/