Solitary potentials in dusty plasmas

Abstract

It is found that a dusty plasma with inertial dust fluid and Boltzmann distributed ions admits only negative solitary potentials associated with nonlinear dust-acoustic waves. The dynamics of small-amplitude disturbances is governed by the Korteweg–de Vries (KdV) equation, the stationary solution of which assumes the inverted bell-shaped secant hyperbolic squared profile. The associated dust and ion density perturbations are, on the other hand, positive. The solitary potentials can be identified as nonlinear structures in low-temperature dusty plasmas such as those in laboratory and astrophysical environments.

Dust ion acoustic solitary structures in presence of nonthermal electrons and isothermal positrons

“…We also assume that the conditions as given in (52) are also true. Consider the condition as given in (53).…”

“…The presence of dust grains having large masses introduces several new aspects in the properties of the nonlinear waves and coherent structures [49][50][51][52][53][54][55][56][57][58][59]. Depending on different time scales, there can exist two or more acoustic waves in a typical dusty plasma.…”

Low-frequency electrostatic dust-modes in a non-uniform magnetized dusty plasma

“…(10) represents a dispersion relation for the dust-acoustic mode modified by the obliqueness and inhomogeneity or dust-drift mode modified by the obliqueness. If we consider parallel propagation or homogeneous dusty plasma system and put Z i = 1 and γ i,e = 1, the dispersion relation reduces to that for the dust-acoustic mode studied by Rao et al [24] and if we further put n e0 = 0 (all electrons are depleted to the surface of the dust grains), this dispersion relation stands for the dust-acoustic waves studied by Mamun et al [32,33] and others [34][35][36]. On the other hand, if we consider perpendicular propagation (k z = 0), this dispersion relation represents the dust-drift mode studied by Shukla et al [42].…”

“…To derive a simple form of the dispersion relation for the dust-lower-hybrid mode, we assume that all electrons are absorbed by the dust-grains [26,32] (i.e., n e0 = 0). Thus, the simplified form of the dispersion relation for the dust-lower-hybrid mode becomes…”

“…The linear and nonlinear properties of these modes are studied by considering a uniform dusty plasma model with or without external magnetic field [30][31][32][33][34][35][36][37][38][39][40][41]. But, in practice, all dusty plasma systems contain some region of inhomogeneity capable of causing drift motions and associated drift waves [42][43][44].…”