2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80566The propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of a model where the material medium is represented by anharmonic oscillators with cubic nonlinearities (Duffing model) and waves can propagate only in the right direction. The system of reduced Maxwell-Duffing equations admits two families of exact analytical solutions in the form of solitary waves. These are bright spikes propagating on a zero background, and bright and dark spikes, propagating on a nonzero background. Direct simulations demonstrate that these pulses are very robust against perturbations. We find that a high frequency modulated electromagnetic pulse evolves into a breather-like one. Conversely a low frequency pulse transforms into a quasi-harmonic wave.pdf-file, 18 pages, 13 figuresPattern Formation and SolitonsExactly Solvable and Integrable Systemstext