  We apply the method of slowly-varying amplitudes of the electrical and magnet
fields to integro-differential system of nonlinear Maxwell equations. The
equations are reduced to system of differential Nonlinear Maxwell amplitude
Equations (NME). Different orders of dispersion of the linear and nonlinear
susceptibility can be estimated. This method allow us to investigate also the
optical pulses with time duration equal or shorter than the relaxation time of
the media. The electric and magnetic fields are presented as sums of circular
and linear components. Thus, NME is written as a set of Nonlinear Dirac
Equations (NDE). Exact solutions of NDE with classical orbital momentum $\ell =
1$ and opposite directions of the spin (opposite charge) $j = \pm1 / 2$ are
obtained. The possible generalization of NME to higher number of optical
components and higher number of $\ell$ and $j$ is discussed. Two kind of Kerr
type media: with and without linear dispersion of the electric and the magnet
susceptibility are consider. The vortex solutions in case of media with
dispersion admit finite energy while the solutions in case of a media without
dispersion admit infinite energy.
