Asymmetric shape and dynamic stability of exciton-phonon solitons moving   in a periodic medium
  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. 
D. Roubtsov (U. of Montreal), Y. Lepine, E. N. Onder