Propagation of extremely short pulses in nonresonant media: the total Maxwell–Duffing model

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell–Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1D bidirectional Maxwell equations. This system of equations has a one parameter family of exact analytical solutions representing an electromagnetic spike propagating on a zero or a nonzero background. We find that the total Maxwell–Duffing equations can be written as a system in bilinear form and that the one-soliton solution of this system coincides with the steady state solution obtained previously.