The traveling relativistic solitons in electron–positron hot plasmas is investigated. The influence of the positron motion on the soliton's structure is taken into account. A closed set of equations consisting of scalar potential, vector potential and enthalpy in ultra-relativistic regime is presented; symmetric and antisymmetric solitary solutions are obtained numerically. The non-linear dispersion relation of the system is derived in the quasi-neutral limit for the purpose of analyzing the modulational instability. Also, the variations of the modulational instability growth rate are investigated. In contrast to the standing solitons, the drifting velocity and plasma fluid velocity of moving solitons both play an important role in the formation of the solutions. In cases where the fluid velocity of the plasma overtakes the drift velocity of the solitary wave, the magnitudes of the scalar and vector potentials increase with the increase of the plasma temperature, otherwise, they decrease. Also compared with single-humped vector potentials, two-humped vector potentials are excited at a lower temperature if the fluid velocity exceeds the soliton drifting velocity.
Electron inertia effect on small amplitude solitons in a weakly relativistic two-fluid plasma