Abstract
In this paper, we establish the existence of four families of simple wave solution for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4 × 4 non-reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0=λ1,λ2,λ3 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.
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