Institute for Studies in Theoretical Physics and Mathematics (IPM),

Farmanieh Building, Farbin Str., Farmanieh Str.,

P.O. Box: 19395-5531, Tehran, IRAN

E-mail: eshraghi@ipm.ir

**On the double Riemann wave solutions in nonrelativistic
and relativistic fluids**

**Abstract:**

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.