Solution of the dusty wave problem for a weak coupling between gas and dust (K = 1) and a dust-to-gas ratio d2g = 1 at times t = 0, 0.2, 0.5, and 2.0. The top panel shows the gas velocity, while the bottom panel shows the dust velocity. The solid lines present numerical solutions at different times as indicated in the legend, while the dashed lines present the corresponding analytical solutions. The two solutions are often almost indistinguishable.