  Solitons are known to move ballistically through a medium without changement
of their shape. In practice, the shape of moving inhomogeneous states changes,
and a long lasting tail appears behind the soliton moving in a periodic medium.
Such a behavior can be described within the model of exciton-phonon coherent
states as a dynamic effect in soliton transport. We argue that the coupling
between bosonic excitations of the medium, such as excitons, and elastic modes
of it, such as phonons, can be responsible for these effects in Condensed
Matter Physics. We derive nonlinear dynamic equations for the excited medium in
the long wavelength approximation (a generalized Zakharov system) and apply a
kind of ballistic ansatz for the coherent state of bosons and displacement
field. The total packet can be associated with an exciton-phonon comet with the
quasistable coherent Bose-core and incoherent tail moving in the medium.
