We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature ðT 6¼ 0Þ where the thermal energy ðKBTÞ and the rest-mass energy ðmec2Þ of electrons do not differ significantly, i.e., be KBT=mec2 ðor Þ 1, but the Fermi energy KBTFÞ and the chemical potential energy ðleÞ of electrons are still a bit higher than the thermal energy, i.e., TF > T and ne ¼ le=KBT 1. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a onedimensional nonlinear Sch€odinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then, we study the MI of the latter in two different regimes, namely, be < 1 and be > 1. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region be > 4. However, for be 1 and 1 < be < 4, the wave can be stable or unstable depending on the values of the EM wave frequency, x, and the parameter ne. We also obtain the instability growth rate for the modulated. wave and find a significant reduction by increasing the values of either be or ne. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov–Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of be 1 and be > 1.
