ИСТИНА

We consider the Riemann problem for the reduction of the complete cold plasma system. The resulting system is inhomogeneous, not strictly hyperbolic, and is not written in a conservative form. Therefore, to construct a solution to the Riemann problem, we must use additional conservation laws inherent in the original model. It turns out that rarefaction waves and delta-singular shock waves replace each other during the oscillation period. For the case of shock waves, we cannot use the traditional Rankine-Hugoniot conditions and therefore we use the relation for the Hugoniot deficit (the amplitude of the delta function) in the spirit of the equations of gas dynamics without pressure. For the case of a rarefaction wave, non-uniqueness is proved and a rule for selecting the correct solution is proposed.