Bifurcation of Small Amplitude Dust-Acoustic Waves in Two-Temperature Ions Dissipative Plasmas

A study of small amplitude dust-acoustic waves is considered in a dissipative plasma system that is composed of mobile dust particles, q-nonextensive distributed cold and hot ions, and immobile electrons. The study is approached within the framework of the nonlinear Burgers equation and the modified Burgers equation, derived through the reductive perturbation technique. Using the wave transformation, the Burgers equation and the modified Burgers equation are transformed into the corresponding dynamical systems. Through the concept of planar dynamical systems, the bifurcation of dust-acoustic waves is studied using the phase plane analysis. By varying the q-nonextensive distribution parameter and the coefficient of viscosity, the changes in the shock waves and periodic waves are examined using numerical simulation. This study may be applicable to understand the dynamics of the dust-acoustic shock and periodic waves in q-nonextensive distributed cold and hot ions that may occur in dissipative plasmas.