A theoretical model is presented to study the characteristics of dust acoustic shock in a viscous, magnetized, rotating dusty plasma at both fast and slow time scales. By employing the reductive perturbation technique, the non-linear Zakharov-Kuznetsov-Burger (ZKB) equation is derived for both cases when the dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow the kappa/Cairns distribution. It is observed that in both cases, i.e. when dust is in the background and active, viscosity plays a key role in dissipation for the propagation of acoustic shock. Magnetic field and rotation are responsible for the dispersive term. Superthermality is found to affect significantly the formation of the shock wave along with viscous nature of plasma, whereas the dust charge affects the non-linear coefficient of the ZKB equation. The present investigation may be beneficial to the understanding of the rotating plasma, in particular the experiments being carried out. K E Y W O R D S dusty plasmas, nonlinear waves, shocks, ZK Burger equation 1 INTRODUCTION Despite a history spanning nearly a century, research into complex (dusty) plasmas (consisting of solid particles of nanometres to hundreds of micrometres size in a conventional two-component plasma) has progressed significantly only in last two decades, mainly after the marvellous observation of dusty plasma crystals by Thomas et al. in 1994. [1] Also, for more than 10 years dusty plasmas under minute gravity conditions have been studied on board the International Space Station (ISS) under the joint Russian/German venture of Plasma Kristall (PK), along with PKE-Nefedov, PK-3 Plus, and PK-42014 onwards. [2] Other than novel experimental discoveries of dusty plasma crystals, dust Mach cones, [3] dust acoustic waves, dust voids, [4] etc., the notion of possible existence of 'dust atoms and molecules' was also put forward by Tsintsadze, Murtaza, and Ehsan. [5] The authors later reported the crystallization of dust atoms in the localized region of the electromagnetic wave. [6] The importance of dusty plasma physics has been manifold, because such plasmas are omnipresent in astrophysical environment like comets, interplanetary or interstellar clouds, the rings of giant planets like Saturn, etc., whereas
