Small amplitude ion-acoustic waves in electron-ion dusty plasma: Landau damping effects of combined Kappa–Cairns distributed electrons

Korteweg–de Vries (KdV) equation with the influence of Landau damping of electrons is developed to explore the weakly nonlinear and weakly dispersive ion-acoustic waves in a non-collisional unmagnetized plasma system whose constituents are adiabatic warm ions, negative-charged immobile dust grains and combined Kappa–Cairns distributed electrons. It is found that the nonlinear coefficient of the KdV equation vanishes along different parametric curves in the parametric space. In this situation, a modified KdV equation with the Landau damping effect is obtained to demonstrate the nonlinear propagation of the ion-acoustic waves. By employing multiple time scale method, the solitary wave solutions of these equations are derived. The solitary wave’s amplitudes have been noticed to decay gradually over time.