On the microscopic theory of the exciton ring fragmentation
  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. 
A.V. Paraskevov, T.V. Khabarova