El-Sayed Mowafy Ahmed «Nonlinear ion acoustic solitary waves in electron-positron inhomogeneous plasma» Вестник Московского университета. Серия 3: Физика. Астрономия, № 3, http://vmu.phys.msu.ru/toc/2016/3 (2016)

A theoretical investigation has been made for studying the propagation of ion-acoustic waves (IAWs) in a weakly inhomogeneous, collisionless, unmagnetized, three-component plasmas, whose constituents are inertial ions, nonthermal electrons, and Boltzmannian positrons. Employing reductive perturbation method (RPM), the variable coefficients Korteweg–de Varies equation (KdV) is derived. At the critical ion density, the KdV equation is not suitable for describing the system. Thus, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. Above (below) this critical point the system supports compressive (rarefactive) solitons. The effect of plasma parameters on the soliton profile has been considered. It has been shown that the width and the amplitude of the soliton affected by wave propagation speed, ratio of positron-to-electron density, and nonthermal parameter.

Abdelwahed H.G., El-Shewy E.K., Aber A.Mahmoud «Time fractional effect on ion acoustic shock waves in ion-pair plasma» Журнал экспериментальной и теоретической физики, 149, № 6, с. 1278-1284 (2016)

The nonlinear properties of ion acoustic shock waves are studied. The Burgers equation is derived and converted into the time fractional Burgers equation by Agrawal's method. Using the Adomian decomposition method, shock wave solutions of the time fractional Burgers equation are constructed. The effect of the time fractional parameter on the shock wave properties in ion-pair plasma is investigated. The results obtained may be important in investigating the broadband electrostatic shock noise in D- and F-regions of Earth's ionosphere.