Geodesic
Rank-$k$ solutions of hydrodynamic-type systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 83-100

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We present a variant of the conditional symmetry method for obtaining rank-$k$ solutions in terms of Riemann invariants for first-order quasilinear hyperbolic systems of PDEs in many dimensions and discuss examples of applying the proposed approach to fluid dynamics equations in $n+1$ dimensions in detail. We obtain several new types of algebraic, rational, and soliton-like solutions (including kinks, bumps, and multiple-wave solutions).
Keywords: conditional symmetry, rank-$k$ solution of partial differential equations.
Mots-clés : Riemann invariant 
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     author = {A. M. Grundland and B. Huard},
     title = {Rank-$k$ solutions of hydrodynamic-type systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a6/}
}
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A. M. Grundland; B. Huard. Rank-$k$ solutions of hydrodynamic-type systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 83-100. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a6/