Geodesic
Exact solutions of the transonic equations of gas dynamics
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 54-63

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The review exact (described by algebraic functions) solutions of a transonic set of Karman–Falkovitch equations is given. Self-similar solutions and two classes of the polynomial-parametrical solutions associated with self-similar at indexes $n=2$ and $n=3$ are considered. Connection with local exposition of singularities of transonic flows is specified, in particular in Laval nozzles. 
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     title = {Exact solutions of the transonic equations of gas dynamics},
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E. O. Kuznetsova; I. A. Chernov. Exact solutions of the transonic equations of gas dynamics. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 54-63. http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a10/