Motion in a one-dimensional (1-D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row. Due to their hydrodynamic interactions, the spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.