Abstract
Symmetry theory is of fundamental importance in studying systems of partial differential equations. At present algebras of classical infinitesimal symmetry transformations are known for many equations of continuum mechanics [1, 2, 4]. Methods foi finding these algebras go back to S. Lie's works written about 100 years ago. Ir particular, knowledge of symmetry algebras makes it possible to construct effectively wide classes of exact solutions for equations under consideration and via Noether's theorem to find conservation laws for Euler–Lagrange equations. The natural development of Lie's theory is the theory of “higher” symmetries and conservation laws [5].
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