Geodesic
Group-theoretical solutions to gas dynamic equations generated by threedimensional Lie subalgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 553-595

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We study group-theoretical solutions to the dynamic equations of polytropic gas. We give a complete list of invariant and partially invariant solutions generated by $3$-dimensional subalgebras of symmetry Lie algebra $L_{13}$. There are $146$ different invariant solutions, $61$ partially invariant solutions, and $12$ types of barochronic solutions in this list. This result is applicable in gas dynamics, aerodynamics, and physics of atmosphere. 
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     author = {A. A. Cherevko},
     title = {Group-theoretical solutions to gas dynamic equations generated by threedimensional {Lie} subalgebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {553--595},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a30/}
}
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A. A. Cherevko. Group-theoretical solutions to gas dynamic equations generated by threedimensional Lie subalgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 553-595. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a30/