The role of dust charge fluctuations on nonlinear dust ion-acoustic waves

The nonlinear propagation of the dust ion-acoustic waves has been investigated accounting for the charge fluctuation dynamics of stationary dust grains in an unmagnetized dusty plasma. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, are derived by employing the reductive perturbation method. It has been shown that dust charge fluctuations produce a dissipation which is responsible for shock waves. Conditions for the formation of dust ion-acoustic solitary and shock waves as well as their properties are clearly explained. The implications of our investigations to both space and laboratory dusty plasmas are discussed.