An exact solution for the potential profile of two coupled one-dimensional arrays each with m junctions with equal junction capacitances C, equal stray capacitances ${\mathit{C}}_{0}$, and equal coupling capacitances ${\mathit{C}}_{\mathit{c}}$ is presented. Analytical expressions for the total free energy as well as the injection threshold voltage ${\mathit{V}}_{\mathit{t}}$ of various charge solitons (an electron-hole pair, a single charge soliton, or a combined electron-hole pair and a single charge soliton) are derived. For m=3, we find that in the weak coupling regime (${\mathit{C}}_{\mathit{c}}$\ensuremath{\ll}C) single electron transport dominates, in contrast with existing results [D. V. Averin et al., Phys. Rev. Lett. 66, 2818 (1991)], and other differences are also found in the ${\mathit{C}}_{\mathit{c}}$\ensuremath{\gg}C limit. \textcopyright{} 1996 The American Physical Society.