Geodesic
Approximate solution of the direct and converse problems of the propagation of a disturbance in a guiding medium
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 5, pp. 1178-1187

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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. 
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     author = {R. P. Tarasov and S. A. Kuchai},
     title = {Approximate solution of~the direct and converse problems of~the propagation of~a~disturbance in~a~guiding medium},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1178--1187},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_5_a9/}
}
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R. P. Tarasov; S. A. Kuchai. Approximate solution of the direct and converse problems of the propagation of a disturbance in a guiding medium. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 5, pp. 1178-1187. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_5_a9/