The Canonical Form of the Rank 2 Invariant Submodels of Evolutionary Type in Ideal Hydrodynamics
- 14 Downloads
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.
Keywordsequations of ideal hydrodynamics state equation admissible subalgebra representation of invariant solution invariant submodel submodel of evolutionary type canonical form of a submodel
Unable to display preview. Download preview PDF.
- 3.S. V. Khabirov, “Optimal Systems of the Sum of Two Ideals as Allowed by Hydrodynamic Type Equations,” Ufim. Mat. Zh. 6 (2), 99–103 (2014).Google Scholar
- 4.Yu. A. Chirkunov and S. V. Khabirov, Elements of Symmetry Analysis of Differential Equations of Continuum Mechanics (Izd. Novosib. Gos. Tekhn. Univ., Novosibirsk, 2012) [in Russian].Google Scholar
- 8.S. V. Khabirov, Analytical Approaches in Gas Dynamics (Izd. Bash. Gos. Univ., Ufa, 1978) [in Russian].Google Scholar
- 10.D. T. Siraeva and S. V. Khabirov, “Invariant Submodel of Rank 2 on a Subalgebra from a Linear Combination of Translations for a Model of Hydrodynamic Type,” Chelyabinsk. Fiz.-Mat. Zh. 3 (1), 38–57 (2018).Google Scholar