  The description is presented for the dependence of the indirect exciton
condensate density at the ring as a function of the polar angle at zero
temperature with the involvement of the processes of formation and
recombination of the excitons. In particular, starting from the quasi
one-dimensional Gross-Pitaevskii equation with a spatially uniform generating
term, we derive an exact analytical solution yielding the fragmentation of an
exciton ring which is probably observed in the experiments.
