Using constant coefficients is an inefficient way to explain the details of the problem of pollutant transport. This is due to factors such as nonuniform geometry, discharge changes, flow velocity and dispersion coefficient variations. Previous studies indicate that the ratio of studies on pollutant transport in rivers is lower than those on the porous media. However, the relative complexity of the solution of the pollutant transport equation in rivers (especially in the case of variable coefficients) in comparison with porous media highlights the importance of focusing on the solutions for rivers environment. In this study, the one-dimensional equation of pollutant transport in the river with location-dependent variables (velocity, dispersion coefficient and cross-section area) with arbitrary pattern is solved via the generalized integral transform technique (GITT) in a finite-length domain and general initial and boundary conditions. In this study, the results obtained from the presented analytical solution are compared to those obtained from the existing analytical solutions in previous studies for the two states of constant and variable coefficients. To further test the accuracy of this method, we have compared the results obtained from the presented analytical solution with the results obtained from numerical solution based on finite-difference method by applying the conditions of two real rivers. Comparison of the results of the GITT verification with available analytical solutions as well as numerical solutions shows the high accuracy and the applicability of the proposed solution considering arbitrary patterns of the ADRE coefficients and general initial and boundary conditions.

使用常数系数是解释污染物运输问题细节的一种无效方法。这是由于几何形状不均匀，流量变化，流速和扩散系数变化等因素引起的。以前的研究表明，河流中污染物迁移的研究比例低于多孔介质。然而，与多孔介质相比，河流中污染物迁移方程解的相对复杂性（尤其是在可变系数的情况下）凸显了关注河流环境解的重要性。在这项研究中，污染物在河流中的一维方程具有位置相关变量（速度，通过有限长度域中的广义积分变换技术（GITT）以及一般的初始和边界条件，可以求解具有任意图案的色散系数和横截面积）。在这项研究中，将从所给出的解析解中获得的结果与从先前研究中针对常数和可变系数的两种状态的现有解析解中获得的结果进行比较。为了进一步检验该方法的准确性，我们通过应用两条真实河流的条件，比较了所提出的解析解和基于有限差分法的数值解的结果。