  We explore a nonlinear field model to describe the interplay between the
ability of excitons to be Bose condensed and their interaction with other modes
of a crystal. We apply our consideration to the long-living paraexcitons in
Cu2O. Taking into account the exciton-phonon interaction and introducing a
coherent phonon part of the moving condensate, we solve quasi-stationary
equations for the exciton-phonon condensate. These equations support localized
solutions, and we discuss the conditions for the inhomogeneous condensate to
appear in the crystal. Allowable values of the characteristic width of
ballistic condensates are estimated. The stability conditions of the moving
condensate are analyzed by use of Landau arguments, and Landau critical
parameters appear in the theory. It follows that, under certain conditions, the
condensate can move through the crystal as a stable droplet. To separate the
coherent and non-coherent parts of the exciton-phonon packet, we suggest to
turn off the phonon wind by the changes in design of the 3D crystal and
boundary conditions for the moving droplet.
