ID: nlin/0309012

Propagation of exremely short pulses in non-resonant media: the total Maxwell-Duffing model

September 4, 2003

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Andrei I. Maimistov, Jean-Guy Caputo
Nonlinear Sciences
Pattern Formation and Solito...
Exactly Solvable and Integra...

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact analytical solutions representing an electromagnetic spike propagating on a zero or a nonzero background. We find that the total Maxwell-Duffing equations can be written as a system in bilinear form and that the one-soliton solution of this system coincides with the steady state solution obtained previously.

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