  We consider a boundary problem for 1D electrodynamics modeling of a pulse
propagation in a metamaterial medium. We build and apply projecting operators
to a Maxwell system in time domain that allows to split the linear propagation
problem to directed waves for a material relations with general dispersion.
Matrix elements of the projectors act as convolution integral operators. For a
weak nonlinearity we generalize the linear results still for arbitrary
dispersion and derive the system of interacting right/left waves with combined
(hybrid) amplitudes. The result is specified for the popular metamaterial model
with Drude formula for both permittivity and permeability coefficients. We also
discuss and investigate stationary solutions of the system related to some
boundary regimes.
