Some models of propagation of extremely short electromagnetic pulses in a nonlinear medium

Some cases of model media considered in this paper allow analytical solutio ns to nonlinear wave equations to be found and the time dependence of the e lectric field strength to be determined in the explicit form for arbitraril y short electromagnetic pulses. Our analysis does not employ any assumption s concerning a harmonic carrier wave or the variation rate of the field in such pulses. The class of models considered includes two-level resonance an d quasi-resonance systems. Nonresonance media are analysed in terms of mode ls of anharmonic oscillators-the Duffing and Lorentz models. In most cases, only particular solutions describing the stationary propagation of a video pulse (a unipolar transient of the electric field or a pulse including a s mall number of oscillations of the electric field around zero) can be found . These solutions correspond to sufficiently strong electromagnetic fields when the dispersion inherent in the medium is suppressed by nonlinear proce sses.