Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

The propagation of linear and nonlinear dustacoustic waves in a homogeneous unmagnetized, collisionlessand dissipative dusty plasma consisted of extremelymassive, micron-sized, negative dust grains hasbeen investigated. The Boltzmann distribution is suggestedfor electrons whereas vortex-like distribution for ions. Inthe linear analysis, the dispersion relation is obtained, andthe dependence of damping rate of the waves on the carrierwave number k, the dust kinematic viscosity coefficient gdand the ratio of the ions to the electrons temperatures ri isdiscussed. In the nonlinear analysis, the modified Korteweg–de Vries–Burgers (mKdV–Burgers) equation isderived via the reductive perturbation method. Bifurcationanalysis is discussed for non-dissipative system in the absenceof Burgers term. In the case of dissipative system, thetangent hyperbolic method is used to solve mKdV–Burgersequation, and yield the shock wave solution. The obtainedresults may be helpful in better understanding of wavespropagation in the astrophysical plasmas as well as in inertialconfinement fusion laboratory plasmas.