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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 1, Pages 83–100
DOI: https://doi.org/10.4213/tmf6072 (Mi tmf6072) 		 
Rank-$k$ solutions of hydrodynamic-type systems

A. M. Grundlandab, B. Huarda

a Université de Montréal, Centre de Recherches Mathématiques
b Université du Québec à Trois-Rivières
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DOI: https://doi.org/10.4213/tmf6072
Abstract: 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, Riemann invariant, rank-$k$ solution of partial differential equations.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 1, Pages 948–962
DOI: https://doi.org/10.1007/s11232-007-0080-6
Bibliographic databases:
Language: Russian
Citation: A. M. Grundland, B. Huard, “Rank-$k$ solutions of hydrodynamic-type systems”, TMF, 152:1 (2007), 83–100; Theoret. and Math. Phys., 152:1 (2007), 948–962
Citation in format AMSBIB
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