Space-time Green function and short pulse propagation in different media

The facilities of using the space-time Green function (GF) for the short pulse propagation analysis were discussed. The GF application reduces a boundary-value problem to an integral calculation, The usefulness of this way is determined by the facilities of an exact and simple enough GF construction and a convenient calculation of obtained integrals. An explicit form of GF can be expressed exactly through the known functions for conducting media, long line and cold plasma without collisions. In other cases it should be calculated approximately. In this work the use of the exact GF form was considered. The propagation of two forms of the pulse was observed. The integral presentation for the rectangular pulse was calculated numerically. The asymptotic expansion was obtained for the pulse where a smallness of the effective pulse time duration was used.