Propagation of localized optical waves in media with dispersion, in dispersionless media and in vacuum. Non-diffracting pulses

The applied method of the amplitude envelopes give us the possibility to describe a new class of amplitude equations governing the propagation of optical pulses in media with dispersion, dispersionless media and vacuum. We normalized these amplitude equations and obtained five dimensionless parameters that determine different linear and nonlinear regimes of the optical pulses evolution. Surprisingly, in linear regime the normalized amplitude equations for media with dispersion and the amplitude equations in dispersionless media and vacuum are equal with precise - material constants. The equations were solved for pulses with low intensity (linear regime), using the method of Fourier transforms. One unexpected new result was the relative stability of light bullets and light disks and the significant reduction of their diffraction enlargement. It is important to emphasize here the case of light disks, which turn out to be practically diffractionless over distances of more than hundred kilometers.