Propagation of Ultra-short Electromagnetic Pulses in a Maxwell-Duffing Medium

We designed a numerical algorithm and conducted numerical simulations aimed at elucidating the role of traveling solitary waves in the pulse dynamics. Our numerical results show that Gaussian-shaped pulses break up into the solitary waves of near preferred velocity; they are followed by some continuous radiation in their wake. The interactions of the simple solitary waves are largely of elastic nature. The phase shift can be observed for all interactions.