Dispersion relation of modulational instability for one-dimensional standing solitary waves in hot ultrarelativistic electron–positron plasmas

In this paper, the non-linear dispersion relation of the system for interactions between high intensity laser and hot relativistic electron–positron plasma is derived. We restrict the problem to the standing solitons in ultrarelativistic plasmas and apply the quasi neutrality condition. The modulational instability growth rate for different values of plasma temperatures, velocities and wave numbers are illustrated numerically. It is shown that,by increasing the unperturbed plasma enthalpy, the modulational instability growth rate decreases for all the values of plasma fluid velocities. It is also found that the growth rate shows an increasing trend with plasma fluid velocity.Furthermore, the impact of wave amplitude on the modulational instability growth rate is investigated explicitly.The growth rate increases with wave number as well as wave amplitude. (author)