The role of dust charging frequency in the linear and nonlinear propagation of dust acoustic waves

The effect of dust charge fluctuation on the existence and propagation of dust acoustic waves in unmagnetized dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. By considering two different limiting cases of the dust charging frequency, it is shown that the dusty plasma system gives rise to linear or nonlinear dust acoustic waves. The well-known collisionless damping of two existing normal modes and one purely damped mode are recovered when the dust charging frequency is comparable to the dust acoustic wave frequency. On the other hand, when the dust charging frequency is considerably higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution.