Propagation of Rarefactive Dust Acoustic Solitary and Shock Waves in Unmagnetized Viscous Dusty Plasma Through the Damped Kadomstev-Petviashvili Burgers Equation

Abstract

AbstractThe non-linear propagation of dust acoustic waves (DAWs) in collisional, unmagnetized, viscous dusty plasma systems containing two temperature ions, electrons, high negatively charged dust grains are investigated. By using the reductive perturbation method (RPM) the damped Kadomtsev-Petviashvili Burgers (dKPB) equation that governs the DAWs is derived. Generally, the impact of viscosity is ignored during the studies of wave dynamics in a plasma medium. In the present investigation, a Burgers term is introduced in order to express the dissipation effect in the viscous plasma circumstance. The strong dissipation due to the presence of Burgers term may cause for rising of a shock solution. However, in a very weak dissipative system, the solitary-like wave solution may arise due to the balance between the dispersion and nonlinearity. Assuming conservation law in the present system, solitary type wave solution is explored, and shock type wave solution is determined by means of Simplified Hirota bilinear method (SHBM). Finally, the effect of the kinematic viscosity, collisional frequency, etc. on wave propagation is demonstrated from numerical understanding.KeywordsDust acoustic wavesReductive Perturbation methodDamped KP-Burgers equationBurgers termShock solutionSolitary like wave solution