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

General equation for directed Electromagnetic Pulse Propagation in 1D metamaterial: Projecting Operators Method