  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 para-excitons in
Cu2O. Taking into account the exciton-phonon interaction and introducing a
coherent phonon part of the moving condensate, we derive the dynamic equations
for the exciton-phonon condensate. These equations can support localized
solutions, and we discuss the conditions for the moving inhomogeneous
condensate to appear in the crystal. We calculate the condensate wave function
and energy, and a collective excitation spectrum in the semiclassical
approximation; the inside-excitations were found to follow the asymptotic
behavior of the macroscopic wave function exactly. The stability conditions of
the moving condensate are analyzed by use of Landau arguments, and Landau
critical parameters appear in the theory. Finally, we apply our model to
describe the recently observed interference and strong nonlinear interaction
between two coherent exciton-phonon packets in Cu2O.
