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To solve the problem of transient electromagnetic wave propagation in unbounded nonlinear medium the Modal Basis Method or Method of Evolutionary Equation is used. It consists in conversion of the initial three-dimensional nonstationary problem to one-dimensional one for set of evolutionary equations with initial and boundary conditions. The construction of the analytical solution of a nonlinear problem in time domain is proposed by the step-by-step method in approximation of weak nonlinearity and losses by taking into account new sources of current.

transient electromagnetic field; time domain; evolutionary approach; nonlinear medium