Interaction of orthogonal-polarized waves in 1D metamaterial with Kerr nonlinearity

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.