Dependence of modulational instability growth rate on the wave number, amplitude of the solitary wave and the non-perturbed temperature of relativistic electron-positron plasma

In this study, the modulational instability growth rate of solitary waves due to the interaction of high-intensity laser with relativistic electron-positron plasma is investigated. The relativistic factor and the density of plasma particles are derived analytically as a function of the scalar and vector potentials, plasma temperature, plasma fluid velocity and soliton velocity, and using it the governing equation of vertical component of electromagnetic wave is derived. The dispersion relation of the system is obtained and the variations of the modulational instability growth rate is investigated numerically. It is shown that the modulational instability depends on the wave number and the amplitude of the solitary wave and the unperturbed plasma temperature. Moreover, it is seen that depending on the relative velocity of the plasma fluid and the solitary wave, modulational instability shows opposing behaviors.