Effects of adiabaticity and non-adiabaticity of dust charge fluctuation on the propagation of the dust ion acoustic waves in inhomogeneous dusty plasma

A theoretical investigation has been made for adiabatic positive and negative dust charge fluctuations on the propagation of dust-ion acoustic waves (DIAWs) in a weakly inhomogeneous, collisionless, unmagnetized dusty plasmas consisting of cold positive ions, stationary positively and negatively charged dust particles and isothermal electrons. The reductive perturbation method is employed to reduce the basic set of fluid equations to the variable coefficients Korteweg–de Vries (KdV) equation. Either compressive or rarefactive solitons are shown to exist depending on the critical value of the ion density, which in turn, depends on the inhomogeneous distribution of the ion. The dissipative effects of non-adiabatic dust charge variation has been studied which cause generation of dust ion acoustic shock waves governed by KdV-Burger (KdVB) equation. The results of the present investigation may be applicable to some dusty plasma environments, such as dusty plasma existing in polar mesosphere region.