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We explore a nonlinear field model to describe the interplay between theability of excitons to be Bose-condensed and their interaction with other modesof a crystal. We apply our consideration to the long-living para-excitons inCu2O. Taking into account the exciton-phonon interaction and introducing acoherent phonon part of the moving condensate, we derive the dynamic equationsfor the exciton-phonon condensate. These equations can support localizedsolutions, and we discuss the conditions for the moving inhomogeneouscondensate to appear in the crystal. We calculate the condensate wave functionand energy, and a collective excitation spectrum in the semiclassicalapproximation; the inside-excitations were found to follow the asymptoticbehavior of the macroscopic wave function exactly. The stability conditions ofthe moving condensate are analyzed by use of Landau arguments, and Landaucritical parameters appear in the theory. Finally, we apply our model todescribe the recently observed interference and strong nonlinear interactionbetween two coherent exciton-phonon packets in Cu2O.Comment: 34 pages, LaTeX, four figures (.ps) are incorporated by epsf.  Submitted to Phys. Rev.

physical review. b, condensed matter

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Bosons in a lattice: Exciton-phonon condensate inCu2O