Application of Adomian decomposition method to study collision effect in dusty plasma in the presence of polarization force

In this article, we studied the approximate analytical soliton solution of dust acoustic waves in the framework of damped Korteg-De Vries (DKdV) equation. Using the reductive perturbation technique, the evolution equation with additional damping term is derived from a collisional dusty plasma model. As the DKdV equation is not integrable, a numerical solution to the DKdV equation is found and is obtained by using the Adomian decomposition method, taking the solution of the standard KdV equation as an initial approximation. The comparison between the current solution with the existing solution proposed earlier by other authors for smaller values of the damping parameter shows a very good agreement between these two. A significant difference in the solution is observed for the higher value of collision frequency. The effect of some relevant plasma parameters on the proposed solution is also analyzed.