Bifurcation Analysis for Dust-Acoustic Waves in a Four-Component Plasma Including Warm Ions

Investigation of linear dust-acoustic (DA) waves was analyzed in a system of collisionless, dissipative, and unmagnetized four-component dusty plasma consisting of cold positively and negatively charged particles of dust, with ions and electrons are of the Boltzmann distribution. The compatibility condition is obtained by using the normal mode analysis. The Korteweg de Vries-Burgers (KdV-Burgers) equation is obtained when the plasma system is nonlinearly analyzed by the reductive perturbation method. To study the nonlinear waves, we obtain some interesting physical solutions. These solutions are in the form of soliton, a combination between a shock and a soliton, and finally monotonic and oscillatory shock waves. Graphical illustration for these solutions was presented. The characteristics of the DA solitary and shock waves are significantly modified by the presence of positive and negative dust ions, the ratio of the ion to electron temperatures, and it is also found that the basic features are affected by the dust kinematic viscosity. The planar dynamical systems bifurcation theory, which was used to establish the existence of solitary wave solutions and periodic traveling wave solutions, has been established. Accordingly, the phase portrait topology and the potential diagram are illustrated for the KdV-Burgers equation. As a result of different phase orbits, there is an advantage to predict different classes of traveling wave solutions. The electric field is determined. Generalization of the obtained results in this paper can be used to investigate the nature of plasma waves in both laboratory and space.