Higher-order corrections to the ion-acoustic waves in a relativistic plasma (isothermal case)

Abstract

As a continuation of our earlier work, we have analysed the higher-order perturbative corrections to the formation of (ion-acoustic) solitary waves in a relativistic plasma. It is found that the relativistic considerations affect the amplitude and width variation - as conjectured in our previous paper. Our analysis employs a higher-order singular perturbation technique, with the elimination of secular terms in stages. In this way we arrive at an inhomogeneous KdV-type equation, which is then solved exactly. At this point a new phenomena arises at a critical value of the phase velocity at which the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched co-ordinate is then used to derive a modified KdV equation. In both cases we have numerically computed the specific physical profile of the new solitary wave and its width.

Study of Ion‐Acoustic Solitary Waves in a Magnetized Plasma Using the Three‐Dimensional Time‐Space Fractional Schamel‐KdV Equation

“…Our conclusions can be considered as a generalization of the model suggested by Nejoh [53] and Pakira and Chowdhury [54] by including the effect of different coefficients. It has been found that the initial superposed solitons travel different distances over a period of time for the different choices of 1 and 2 and that the solitonic amplitude increases with an increase in the 2 / 1 ratio.…”

“…and are the right-sided Caputo fractional differential operators of orders and , respectively. Therefore, the adjoint equation (54) can be rewritten as * = ( )…”

Weakly relativistic solitons in a magnetized ion-beam plasma in presence of electron inertia

“…The invariance of relativistic Maxwell equilibrium distribution function was investigated by Synge 11 in the long past. Many workers such as Das and Paul, 12 Nejoh, 13 Das et al, 14 Pakira et al, 15 Kuehl and Zhang, 16 Nejoh, 17 Malik et al, 18 Chatterjee and Roychoudhury, 19 El-Labany and Shaaban, 20 Kalita et al, 21 and Roychoudhury et al 22 have investigated the existence of ion-acoustic solitary waves under various physical situations in relativistic plasmas. But all these investigations are made in unmagnetized plasmas with relativistic effect.…”

Effects of ion and electron drifts on large amplitude solitary waves in a relativistic plasma

“…During the last two decades or so, some authors have studied ion acoustic solitary waves in relativistic plasmas. [9][10][11][12][13] It was Roychoudhury and Bhattacharyya 14 who first found the exact pseudopotential for a relativistic plasma. They, however, neglected the electron inertia.…”