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Dromions are exact nonlinear solutions of a large class of two-dimensional (2-D) partial differential equations and may be considered as an extension of the familiar soliton solutions to the 2-D space. They have stable localized structures with an exponential decay in both space dimensions and are characterized by time-dependent boundary conditions. While solitons have been used extensively to model coherent wave phenomena in plasmas, dromions have received little attention in terms of application to experimental observations. In a recent paper, we have shown that the nonlinear evolution of a 2-D electron acoustic wave in auroral plasma may lead to dromion solutions whose shape and size can be consistent with those of monopolar and bipolar pulses observed by the high resolution measurements of POLAR and FAST satellites. The previous theoretical analysis is extended to examine the time evolution of the dromion solution, study its stability, and discuss its boundary conditions in the context of auroral plasmas. The effect of different parameters on the shape and size of the dromion solutions is also estimated.