A hyperbolic model for the one‐dimensional electromagnetic pulse

An account of the current phenomenology relative to the electromagnetic pulse is obtained by having recourse to the model of a charged fluid. In particular, a differential system is deduced for the description of a one‐dimensional electric field generated by the so‐called Compton current. The system turns out to be hyperbolic, thus allowing for discontinuity waves. The evolution law for the amplitude of such waves is examined in detail. Mathematical problems resulting from vanishing of the electric field ahead of the wave front are also investigated.