Influence of higher-order terms of the approximate dispersion theory on the pulse envelope profile in a dispersive medium

Results of the numerical calculation of the envelope and frequency profile of a pulse propagating in a dispersive medium, exemplified by the propagation of a femtosecond pulse in the plasma, are presented. The explanation for the appearance of modulation in the odd orders of approximation of the theory of dispersion and for the extinction of modulation in the even orders is given. Taking into account the fourth-order term of the approximate dispersion theory is shown to be sufficient in the majority of cases when calculating the ultrashort pulse propagation.