Geodesic
Equations of gas dynamics admitting an infinite number of symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 2, pp. 163-171

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All the equations of state are found for which the one-dimensional gas dynamic equations possess an infinite Lie–Backlund algebra. In all these cases the gas dynamics equations are either explicitely integrable or can be presented in the Lax form. A method for constructing an infinite set of conservation laws is given. 
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     author = {A. G. Meshkov and B. B. Mikhalyaev},
     title = {Equations of gas dynamics admitting an infinite number of symmetries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {2},
     year = {1987},
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A. G. Meshkov; B. B. Mikhalyaev. Equations of gas dynamics admitting an infinite number of symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 2, pp. 163-171. http://geodesic.mathdoc.fr/item/TMF_1987_72_2_a0/