Geodesic
Symmetries and solutions to equations of two-dimensional motions of polytropic gas
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 291-307

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The optimal system of subalgebras for the $9$-dimensional Lie algebra was constructed. This system classifies invariant submodels of equation governing the motion of polytropic gas with polytrope-exponent $\gamma=2$. Invariant submodels of rank equal to 0 were found and their physical properties were described. 
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     author = {A. S. Pavlenko},
     title = {Symmetries and solutions to equations of two-dimensional motions of polytropic gas},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {291--307},
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     volume = {2},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/}
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A. S. Pavlenko. Symmetries and solutions to equations of two-dimensional motions of polytropic gas. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 291-307. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/