Closed form solutions to water pollution problems using auto-BäcklundTransformations

Abstract

Air pollution can be very harmful to human health, especially in urban areas of large cities and in the vicinity of chemical industries. In order to prevent and minimize environmental impacts from these industries, it is necessary to use mathematical models, which can simulate scenarios associated with dispersion of pollutants. This work presents a new analytical method for solving pollutant dispersion problems. The method uses two first-order differential restrictions from which are found auto-Bäcklund transformations for the two-dimensional advection-diffusion equation at steady state. The main characteristic of the formulation is the reduced time required to obtain analytical solutions.