Wave packets in an absorptive and strongly dispersive medium

The evolution of slowly varying wave pulses in strongly dispersive and absorptive media is studied by a recursive method. It is shown that the resulting envelope function may be obtained by including correction terms of arbitrary dispersive and absorptive orders. Different definitions of pulse velocity are discussed in some detail and finally, qualitative examples of a Gaussian pulse in a cold plasma and an atomic medium are given, illustrating the importance of higher-order terms in the velocity expression. Particularly, the packet velocity is shown to be dependent on pulse width besides dispersion.