Nonlinear waves in nonplanar and nonuniform dusty plasmas

The nonlinear properties of the dust acoustic solitary wave and shock wave in inhomogeneous nonplanar dusty plasmas are considered theoretically and numerically. The effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium particle density, nonuniform equilibrium charging, and nonplanar geometry on waves are presented. When τch/τd is small but finite, where τch is the charging time scale and τd is the hydrodynamical time scale, a variable coefficients nonplanar Korteweg-de Vries (KdV) Burgers equation governing the nonlinear waves is derived by the perturbation method. The analytical expressions for the evolution of soliton and shock wave (both oscillatory and monotone shock) are obtained and the theoretical results are confirmed by the numerical solution of the nonlinear wave equation