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Journal of Applied and Industrial Mathematics

, Volume 13, Issue 2, pp 340–349 | Cite as

The Canonical Form of the Rank 2 Invariant Submodels of Evolutionary Type in Ideal Hydrodynamics

  • D. T. SiraevaEmail author
Article

Abstract

The equations of ideal hydrodynamics are considered with the state equation in the form of the pressure represented as the sum of density and entropy functions. Some twelve-dimensional Lie algebra corresponds to the admissible group of transformations. Basing on the two-dimensional subalgebras of the Lie algebra, we construct the rank 2 invariant submodels of canonical form and evolutionary type. The form is refined of the rank 2 invariant submodels of canonical form and evolutionary type for the eleven-dimensional Lie algebra admitted by the gas dynamics equations with the state equation of the general type.

Keywords

equations of ideal hydrodynamics state equation admissible subalgebra representation of invariant solution invariant submodel submodel of evolutionary type canonical form of a submodel 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Mavlyutov Institute of MechanicsUfaRussia

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