Abstract
The nonlinear propagation of electrostatic dust-acoustic waves is studied in an unmagnetized three-component dusty plasma consisting of negatively charged dust, free as well as a small percentage of trapped ions and Maxwellian electrons. By using the reductive perturbation technique, a Korteweg de Vries type equation, which governs the dynamics of the small-amplitude solitary and periodic waves of the dusty plasma under consideration, is derived. The traveling soliton (shown to be only of the rarefactive type) and periodic solutions of the KdV type equation are obtained. Bifurcation analysis for the obtained nonlinear KdV type equation is used to describe the qualitative phase portrait for the corresponding dynamical system, which is found to be controlled by the plasma system parameters. The effects of trapped ions and free electrons on the dust-acoustic solitons and periodic waves are discussed. The present investigation may be useful in understanding some nonlinear features of the dust-acoustic waves, which have been observed in astrophysical plasmas such as Saturn's moon Enceladus.