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On the double Riemann wave solutions in nonrelativistic and relativistic fluids

Usual Riemann wave is an exact one dimensional solution of fluid equations. A first generalization of this solution is a multidimensional simple wave. A further non-trivial generalization is a double wave in which there are two coupled but independent phases. In this work a development of this solution is given to obtain the time of discontinuity formation. In presenting this solution for relativistic flows, it is demonstrated the initial conditions must satisfy a specific equation. Also the existence of Riemann invariants is investigated through characteristic surfaces.