Abstract
The propagation of nonlinear dust-acoustic waves (DAWs) in an unmagnetized, collisionless dusty plasma consisting of dust grains obeying the power-law dust size distribution and nonthermal ions are investigated. For nonlinear DAWs, a reductive perturbation method was employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. As the wave amplitude increases, the width and the velocity of the soliton deviate from the prediction of the KdV equation, i.e. the breakdown of the KdV approximation occurs. To overcome this weakness, we extended our analysis to obtain the KdV equation with the fifth-order dispersion term. After that, the higher order solution for the resulting equation has been achieved via what is called the perturbation technique. The effects of dust size distribution, dust radius and nonthermal distribution of ions on the higher order soliton amplitude, width and energy of electrostatic solitary structures are presented.