Analysis of solitons structure of the damped KdV equation arising in superthermal plasmas: Application of homotopy analysis method

Abstract

AbstractThe aim of the proposed work is to analyze the soliton structures of dust‐ion acoustic waves obtained in the framework of the Korteg‐de Vries (KdV) equation with the presence of a damping term. The concept of electron acoustic solitary wave in an unmagnetized plasma consisting of superthermal electrons has been taken into consideration. The KdV equation with the presence of a damping term has been derived with the help of the reductive perturbation technique and solved by using the well‐known homotopy analysis method. The considered method approximates all problems in a straightforward and simplified manner. The method computes the series solution efficiently and provides a simple way to ensure its convergence. The approximate analytical solution obtained from the present analysis is compared with available results in the literature for a different choice of pertinent parameters. The upshots specified that the amplitude of solitary waves increases for increasing values of the damping parameter. This study would in a way to demonstrate the potential and effectiveness of the homotopy analysis method to evaluate the various kinds of nonlinear equations arising in the soliton theory.