Geodesic
Riemann-invariant solutions of the~isentropic fluid flow equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 399-410

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We use a new version of the conditional symmetry method to obtain rank-$k$ solutions expressed in terms of Riemann invariants of the isentropic compressible ideal fluid flow in $3+1$ dimensions. We describe the procedure for constructing bounded solutions in terms of the elliptic Weierstrass $\wp$-function in detail.
Mots-clés : Riemann invariant
Keywords: conditional symmetry method, rank-$k$ solution, system of hydrodynamic type. 
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     author = {R. Conte and A. M. Grundland and B. Huard},
     title = {Riemann-invariant solutions of the~isentropic fluid flow equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {159},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a6/}
}
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R. Conte; A. M. Grundland; B. Huard. Riemann-invariant solutions of the~isentropic fluid flow equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 399-410. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a6/