Propagation of exremely short pulses in non-resonant 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 1-d 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.