Dust-Acoustic Multi-solitons and Shock in a Polarized Space Dusty Plasma Using Darboux Transformation

The properties of dust acoustic waves(DAWs) in a dusty plasma containing Cairns-Tsallis (C-T) distributed ions, Boltzmann distributed electrons, and negatively charged dust particles in the presence of a polarization force are investigated. The Burger equation is derived from the fluids equation of the plasma system with the help of the reductive perturbation technique(RPT). The Lax-pair of the evolution equation in obtained and the characteristic of the DAWs are investigated by employing the Darbox transformation. Some new waves are observed (one soliton, two soliton-shock etc.) as the Darboux transformation is used through the Lax pair. It is also shown that the propagation of nonlinear waves are significantly affected by the physical plasma parameters.