Dust acoustic shock waves in dusty plasma of opposite polarity with non-extensive electron and ion distributions

Abstract

A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.

Analytical Wave Solutions for Foam and KdV-Burgers Equations Using Extended Homogeneous Balance Method

“…For example, solutions (45) and (70) are sinusoidal-type periodical solutions shown in Figure 1, and the rational solutions are (39) and (74), which may be helpful to explain certain physical phenomena, while solutions (50) and (73) are explosive/blow up solutions [1,34] (see Figure 2). The solutions (49) and (72) are shock wave solutions as depicted in Figure 3, note here that the shock wave solution of the foam drainage equation has an important role to describing the motion in the foam while the shock wave solution of the KdV-Burgers equation is very important for studying the acoustic waves in plasma physics as in [29,30] where the dust acoustic shock waves have been studied. The solution (77) represents a soliton wave (Figure 4) which plays a great role in the study of plasma physics [35][36][37].…”

“…The KdV-Burgers equation [27][28][29] is a very common and important equation in studying solitary waves and acoustic waves in plasma physics [30]. Shock waves due to thde KdV-Burgerss equation were observed in dusty plasma by Nakamura et al [31] and Masoad et al [32].…”

Low-frequency shock waves in a magnetized superthermal dusty plasma

“…Since most of the space and astrophysical plasmas are permeated by magnetic field, the effect of external magnetic field on electrostatic solitary waves in different kinds of plasma environments has been studied by various authors [41][42][43][44][45][46][47][48][49][50][51][52][53]. The obliquely propagating ion-acoustic (IA) solitons in a magnetized and weakly relativistic warm plasma have been investigated by deriving KdV equation and it was inferred that the soliton energy is lowered by stronger magnetic field and the solitons become narrower [41].…”

“…Shahmansouri and Mamun [52] studied the dust acoustic shock waves in magnetized nonthermal dusty plasma. Zaghbeer et al [53] reported the study of dust acoustic shocks in magnetized dusty plasma with nonextensive electrons and ions. The KdV-Burgers equation was derived by using reductive perturbation method and found that DA shocks are significantly modified by the combined effects of dust fluid viscosity, external magnetic field and obliqueness.…”

Progress of nonlinear Dust Acoustic Waves in Dust Plasma of Opposite Polarity

“…Recently, El Wakil [13] investigated theoretically the higherorder contributions to nonlinear dust-acoustic waves that propagates in a mesospheric dusty plasma with a completely depletion of background (electrons and ions). However, in most space dusty plasma systems a complete depletion of the background electrons and ions is not possible [14][15][16][17] and the positive dust component is of finite temperature [18,19]. Later, Attia et.…”