In the two component relativistic plasmas subject to pressure variation of adiabatic electrons and isothermal ions, both compressive and rarefactive KdV solitons are established in a quite different physical plasma model. It is desirable to define c s in a new way to substantiate the validity of the model under relativistic effects. The corresponding mathematical condition is also determined, which is a new report of this kind. It is also interesting to report that the relativistic rarefactive solitons cease to exist below some critical ion initial streaming speed v i0 for a fixed temperature α and electron streaming speed v e0. Besides, higher initial flux v i0 of ions under constant temperature is observed to generate higher speed v i at the passage of time which causes to increase (in relativistic sense) its mass diminishing thereby the growth of soliton amplitudes.