  Using a nonlinear Schr\"odinger equation including short-range two-body
attraction and three-body repulsion, we investigate the spatial distribution of
indirect excitons in semiconductor coupled quantum wells. The results obtained
can interpret the experimental phenomenon that annular exciton cloud first
contracts then expands when the number of confined excitons is increased in
impurity potential well, as observed by Lai \emph{et al.} [Lai $et al.$,
Science \textbf{303}, 503 (2004)]. In particular, the model reconciles the
patterns of exciton rings reported by Butov \emph{et al.} [Butov $et al.$,
Nature \textbf{418}, 751 (2002)]. At higher densities, the model predicts much
richer patterns, which could be tested by future experiments.
