Kazantseva Elena V, Maimistov Andrei I, Caputo Jean-Guy
Department of Solid State Physics, Moscow Engineering Physics Institute, Kashirskoe sh. 31, Moscow 115409, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):056622. doi: 10.1103/PhysRevE.71.056622. Epub 2005 May 31.
The propagation of extremely short pulses of an electromagnetic field (electromagnetic spikes) is considered in the framework of a model wherein 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. We find that these steady-state pulses are stable in terms of boundedness of the Hamiltonian. 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 quasiharmonic wave.
