Investigation of dust ion acoustic shock and solitary waves in a viscous dusty plasma

A viscous dusty plasma containing Kappa-(κ - ) distributed electrons, positive warm viscous ions, and constant negatively charged dust grains with viscosity have been considered to study the modes of dust-ion-acoustic waves (DIAWs) theoretically and numerically. The derivations and basic features of shock and solitary waves with different plasma parameters like Mach number, finite temperature coefficient, unperturbed dust streaming velocity, the kinematic viscosity of dust, etc of this DIAWs mode have been performed. Considering the dynamical equation from Korteweg-de Vries(KdV) equation, a phase portrait has been drawn and the position of the saddle point or col. and center have also been discussed. This type of dusty plasma can be found in celestial bodies. The results of this research work can be applied to study the properties of DIAWs in various astrophysical situations where κ-distributive electrons are present and careful modification of the same model can help us to understand the nature of the DIAWs of laboratory plasma as well.