  We consider a propagation of exotermic transition front in a discrete
conservative oscillatory chain. Adequate description of such fronts is a key
point in prediction of important transient phenomena, including phase
transitions and topochemical reactions. Due to constant energy supply, the
transition front can propagate with high velocities, precluding any
continuum-based considerations. Stationary propagation of the front is
accompanied by formation of a non-stationary oscillatory tail with complicated
internal structure. We demonstrate that the structure of the oscillatory tail
is related to a relationship between phase and group velocities of the
oscillations. We suggest also an approximate analytic procedure, which allows
one to determine all basic characteristics of the propagation process: velocity
and width of the front, frequency and amplitude of the after-front
oscillations, as well as the structure of the oscillatory tail. As an example,
we consider a simple case of biharmonic double-well on-site potential. Numeric
results nicely conform to the analytic predictions.
