Abstract

In this work, using inverse scattering techniques, the evolution of the single-soliton solution of the Korteweg-de Vries equation in the presence of perturbations is analyzed. The evolution of the scattering data is found for the Sturm-Liouville operator, the potential of which is a solution to the perturbed Korteweg-de Vries equation.The results obtained are illustrated with an example.The results can be applied to studying the process of wave propagation on shallow polluted waters.