Approximate solution of the direct and converse problems of the propagation of a disturbance in a guiding medium

The direct and converse problems of electromagnetic pulse propagation in media, invariant to shifts in the direction of propagation, are considered. In the case of a homogeneous space with conductivity, the technique of fractional powers of an operator is used to transform from a second-order equation in the propagation coordinate to a first-order equation, and the problems are written as direct and converse Cauchy problems. Methods for the approximate solution are based on different exponential representations of the operator of the semi-group generated by the Cauchy problem. Results of a numerical experiment are quoted.