We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration $C(x, t)$ in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions 𝑥 ≤ 0 and 𝑥 ≥0 and the origin at 𝑥 = 0. The variation of $C(x, t)$ with the time 𝑡 from 𝑡 = 0 up to 𝑡 $\rightarrow \infty $ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient 𝐷 = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.
