Pulse propagation in dispersive media

We give a simple formula for the calculation of the moments of a propagating pulse in a dispersive medium. Both the spatial and time moments are considered. Explicit formulas are derived for the spatial spreading of a propagating pulse and also for the duration of the pulse at a fixed position in space. In addition, we give formulas for the calculation of the instantaneous frequency of a pulse at a given position. A number of simple examples are used to illustrate the formulas derived.