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.
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