ultra-relativistic solitons with opposing behaviors in photon gas plasma

We have studied the formation of relativistic solitary waves due to nonlinear interaction of strong electromagnetic wave with the plasma wave. here, our plasma is relativistic both in temperature and in streaming speed. a set of equations consisting of scalar and vector potentials together with a third order equation for the enthalpy in photon gas plasma is obtained analytically. solutions with single-humped for the scalar potential and single and double-humped for the vector potential profiles are illustrated numerically. it is shown that the drifting velocity of moving solitons and plasma fluid velocity both play an important role in the formation of the solutions. the results show that the amplitude of the potentials increases for higher values of the plasma temperatures for the region that the flow velocity of the plasma is larger than the solitary wave velocity. for the region with larger amount of the soliton's velocity, the results show opposite behavior. it is also found that in the region where the plasma fluid velocity exceeds the soliton drifting velocity, all the solutions are excited at higher temperatures relative to the other area.