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

The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number k, the dust kinematic viscosity coefficient gd and the ratio of the ions to the electrons temperatures ri is discussed. In the nonlinear analysis, the modified Korteweg– de Vries–Burgers (mKdV–Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV–Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.