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).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 83–100, July, 2007.
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Grundland, A.M., Huard, B. Rank-k solutions of hydrodynamic-type systems. Theor Math Phys 152, 948–962 (2007). https://doi.org/10.1007/s11232-007-0080-6
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DOI: https://doi.org/10.1007/s11232-007-0080-6