Abstract
Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.