Linear and nonlinear dust-acoustic waves in inhomogeneous dusty plasmas

The propagation of linear, as well as nonlinear, dust-acoustic waves in inhomogeneous dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. It is shown that the amplitude of the dust-acoustic waves is affected by the presence of the dust density inhomogeneity. Amplitudes of the linear and nonlinear dust-acoustic waves decrease (increase) as the waves propagate in the direction of increasing (decreasing) density. The wave amplitude is inversely proportional to the square root of the dust particle’s density for the linear dust-acoustic waves. In the nonlinear case, to the lowest order and for the cold dust species, the wave amplitude is found to be directly proportional to $n_{\text{d0}}^{\text{−1/4}}.$ Various special cases are explicitly considered, and comparison with the corresponding results for the usual two-component electron-ion plasmas is also carried out.