Fluid transport is a very common phenomenon. Recently flow process in nanochannels has drawn much attention, since it differs quite much from that in macroscopic pipes. In particular, the motion of confined water molecules in nonpolar nanochannels has become a hotspot in nanotechnology, and also an important issue in biology and chemistry. Besides the experimental studies, computer simulations (e.g., molecular dynamics simulation) have also been proven to be a powerful tool to investigate such issues. Early simulations focused on the concurrent motion of all water molecules inside nanochannels such as carbon nanotubes (CNTs), where water molecules are evenly spaced in a single file and occasionally but collectively transport through CNTs. Recently, a new model of water transport in CNTs was presented, which indicates that water-density defects in the one-dimensional (1D) chain of water molecules can move as solitons. This is explained as a natural consequence of competition between water-water interactions and water-CNT interactions. While this new model is very appealing, the identification of soliton is not a trivial work (especially at not very low temperatures), since the density defects of water molecules might not be easily recognized from their thermal fluctuation. In this paper, a new method is developed to precisely identify the soliton by quenching the simulation conformations to their nearest neighboring local minima. Based on the new soliton identification method, we study the motion of water in single-walled armchair CNTs by all-atom molecular dynamics simulations. We investigate the motion of solitons in detail, which is observed as a standard 1D diffusion on a picosecond time scale. The simulations also show that the diffusion coefficient of solitons increases with temperature rising, and decreases with the number density of solitons increasing. These results are consistent with the postulation that there exists a weak repulsion between solitons.