  The dispersion of small amplitude, impulsively excited wave trains
propagating along a magnetic flux tube is investigated. The initial disturbance
is a localized transverse displacement of the tube that excites a fast kink
wave packet. The spatial and temporal evolution of the perturbed variables
(density, plasma displacement, velocity, ...) is given by an analytical
expression containing an integral that is computed numerically. We find that
the dispersion of fast kink wave trains is more important for shorter initial
disturbances (i.e. more concentrated in the longitudinal direction) and for
larger density ratios (i.e. for larger contrasts of the tube density with
respect to the environment density). This type of excitation generates a wave
train whose signature at a fixed position along a coronal loop is a short event
(duration ~ 20 s) in which the velocity and density oscillate very rapidly with
typical periods of the order of a few seconds. The oscillatory period is not
constant but gradually declines during the course of this event. Peak values of
the velocity are of the order of 10 km/s and are accompanied by maximum density
variations of the order of 10-15% the unperturbed loop density.
