Motivated by the experiment of electrostatic conveyor belt for indirect
excitons [A. G. Winbow, \textit{et al.}, Phys. Rev. Lett. \textbf{106},
196806 (2011)], we study the exciton patterns for understanding the exciton
dynamics. By analyzing the exciton diffusion, we find that the patterns
mainly come from the photoluminescence of two kinds of excitons. The patterns near the laser spot
come from the hot excitons which can be regarded as the classical particles.
However, the patterns far from the laser spot come from the cooled excitons
or coherent excitons. Taking into account of the finite lifetime of Bosonic
excitons and of the interactions between them, we build a time-dependent
nonlinear Schr"{o}dinger equation including the non-Hermitian dissipation
to describe the coherent exciton dynamics. The real-time and imaginary-time
evolutions are used alternately to solve the Schr"{o}dinger equation in
order to simulate the exciton diffusion accompanied with the exciton cooling in
the moving lattices. By calculating the escape probability, we obtain the
transport distances of the coherent excitons in the conveyor which are
consistent with the experimental data. The cooling speed of excitons is
found to be important in the coherent exciton transport. Moreover, the
plateau in the average transport distance cannot be explained by the
dynamical localization-delocalization transition induced by the disorders.