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PROPAGATION OF SPIKES IN NONRESONANT ATOMIC MEDIA: THE REDUCED MAXWELL-DUFFING MODEL

We obtain spikes or extremely short pulses for reduced Maxwell-Duffing equations under a general boundary condition, connecting the electric field and electron amplitude, using a Möbius transformation. For a nonzero background, this system is shown to admit two families of exact solutions in the form of solitary waves and kink-type of solutions. Parameter domains are delineated where localized solutions signifying both bright and dark spikes, as also singular solutions indicating self-focusing effect, exist in this dynamical system, in nonresonant atomic media.