Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

The nonlinear properties of small amplitude dust-acoustic solitary waves (DAWs) in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. The effects of the presence of charged hot and cold dust grains on the nature of DAWs were discussed. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.