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Mechanics
Simple solutions of rank 2 invariant submodel for monatomic gas
S. V. Khabirovab, R. F. Shayakhmetovaa a Ufa State Aviation Technical University, Ufa, Russia
b Mavlyutov Institute of Mechanics of Ufa Federal Research Centre of RAS, Ufa, Russia
Abstract:
We consider the invariant submodel of rank 2 on two-dimensional subalgebra containing the projective operator and the dilatation operator with respect to the thermodynamic parameters of a monatomic gas. The submodel is written in the canonical form, therefore, the representation of the solution has a nontrivial form. Invariant solutions, irrotational motions, and a series of simple solutions with differential relations are obtained. The gas motions are without collapse on the whole space. Gas is compressed at first, and then it is dispersed to the vacuum. Soliton-like movements of gas bunch have also been found.
Keywords:
monatomic gas, invariant submodel, differential relations, solitary density waves.
Received: 08.05.2018 Revised: 11.06.2018
Citation:
S. V. Khabirov, R. F. Shayakhmetova, “Simple solutions of rank 2 invariant submodel for monatomic gas”, Chelyab. Fiz.-Mat. Zh., 3:3 (2018), 353–373
Linking options:
https://www.mathnet.ru/eng/chfmj112 https://www.mathnet.ru/eng/chfmj/v3/i3/p353
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Abstract page: | 130 | Full-text PDF : | 31 | References: | 24 |
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