The Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in a Dusty Plasma with Nonthermal Ions Distribution

Abstract

Propagation of nonlinear dust-acoustic (DA) waves in a unmagnetized collisionless mesospheric dusty plasma containing positively and negatively charged dust grains and nonthermal ion distributions are investigated. For nonlinear DA waves, a reductive perturbation method is employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. As it is well-known, KdV equations contain the lowest-order nonlinearity and dispersion, and consequently can be adopted for only small amplitudes. As the wave amplitude increases, the width and velocity of a soliton can not be described within the framework of KdV equations. So, we extend our analysis and take higher-order nonlinear and dispersion terms into account to clarify the essential effects of higher-order corrections. Moreover, in order to study the effects of higher-order nonlinearity and dispersion on the output solution, we address an appropriate technique, namely the renormalization method.

Dust ion‐acoustic solitons collision in weakly relativistic plasmas with superthermality‐distributed electrons and positrons: Higher‐order phase shifts

“…[30][31][32][33][34] For this reason, the KdVEs with the fifth-order dispersion terms are applied to obtain the following equations [30,32] : H-O approximations of the reductive perturbation method are taken into account for their more accurate description and analysis.…”

“…It is obvious that in the pulsar magnetosphere, the ions having streaming velocities approach to the velocity of light. [30][31][32][33] Basically, this method depends on the H-O approximation of the reductive perturbation analysis. Furthermore, it is well established that the temperature (mass) of dust grains is much less (much more) than the temperature (mass) of ions, electrons, and positrons.…”

Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

“…such differences in sign of the charge on the dust grains can greatly modify the properties of the plasma. Recently, some papers have been devoted before to study a theoretical models for the existence of both two types of dust fluids in a homogeneous (inhomogeneous) plasma, see for example (El-Wakil et al 2006;Mowafy et al 2008;Abdelwahed et al 2008;Mamun and Shukla 2002;Sayed and Mamun 2007;Mamun 2008;El-Shewy et al 2008). Akhtar et al (2007), derived the Sagdeevs pseudopotential for dust acoustic waves (DAWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Boltzmannian ions and electrons, and studied the existence of rarefactive solitons.…”