2003/09/22 by Elena V. Kazantseva, Kazantseva, Elena V., Andrei I. Maimistov +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0309057
pdf-file, 18 pages, 13 figures
arxiv created 2003/09/22 · arxiv updated 2009/12/01
The 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.