A statistical-thermodynamic theory of the phenomenon of stimulated amplific
ation of the population of excitons which lie at the bottom of their lowest
-energy band is presented. The experimentally detected "packet" of excitons
flowing ballistically is shown to consist of a Schrodinger-Davydov solitar
y wave, dressed with a cloud of incoherent excitons. Moreover, a secondary
excitation by a c.w. laser beam promotes a Frohlich-Bose-Einstein-like cond
ensation, which is responsible for the relevant phenomenon that the lifetim
e of the soliton is largely increased with increasing pumping power.