The application scope of the reductive perturbation method and the upper limit of the dust acoustic solitary waves in a dusty plasma

Abstract

The dust acoustic solitary waves have been numerically investigated by using one dimensional electrostatic particle-in-cell method. By comparing the numerical results with those obtained from the traditional reductive perturbation method, it is found that there exist the maximum dimensionless amplitude and propagation speed of the dust acoustic solitary wave. And these limitations of the solitary wave are explained by using the Sagdeev potential technique. Furthermore, it is noticed that although ϵ ≪ 1 is required in the reductive perturbation method generally, the reductive perturbation method is also valid for ϵ < 1 in a dusty plasma, which may be extended to branches where the reductive perturbation method is used.