الفهرس 
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Abstract
Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method was employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation. At the critical hot dusty plasma density, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates was considered to derive the modified KdV equation. It was found that the presence of hot and cold dust charge grains does not only significantly modify the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV (fmKdV) equation was derived, which admits both soliton and double layer solutions. A theoretical investigation was carried out for contribution of the higher-order nonlinearity. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge grains are found to significantly change the higher-order properties (viz. the amplitude and width) of the DASWs. For two dimensional small amplitude dust-acoustic solitary waves (DAWs), the Kadomstev- Petviashvili (KP) equation was obtained and the energy of two temperatures charged dusty grains were computed. In the presence of kinematic viscosity, The KdV-Burgers, mKdV-Burgers and Burgers equations were derived. It is found that solitary and shock waves can be produced in this medium. The effects of important parameters such as hot and cold dust charge and density parameters on the properties of shock waves are discussed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments such as Saturn’s F-ring.