Geodesic
Simple solutions of rank 2 invariant submodel for monatomic gas
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 353-373

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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. 
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     author = {S. V. Khabirov and R. F. Shayakhmetova},
     title = {Simple solutions of rank 2 invariant submodel for monatomic gas},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {353--373},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a8/}
}
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S. V. Khabirov; R. F. Shayakhmetova. Simple solutions of rank 2 invariant submodel for monatomic gas. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 353-373. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a8/