  A theoretical study of wave propagation in 1D metamaterial is presented. A
system of nonlinear evolution equation for electromagnetic waves with both
polarizations account is derived by means of projection operators method for
general nonlinearity and dispersion. The system describes interaction of
opposite directed waves with a given polarization. The particular case of Kerr
nonlinearity and Drude dispersion is considered. In such approximation it
results in the correspondent systems of nonlinear equations that generalizes
the Sch\"{a}fer-Wayne one. Particular solutions in case of slow-varying
envelopes are found, plotted and analyzed in gigahertz range. Travelling wave
solution for the system of equation of interaction of orthogonal-polarized
waves is also obtained and the correspondent nonlinear dispersion relations are
written in explicit form.
