Weakly Relativistic Ion-Acoustic Solitary Waves in Dusty Plasma

Abstract

The streaming speeds of relativistic electrons ( $v_{e0})$ and ions ( $v_{i0})$ together with the negative dust charge $Z_{d}$ of immobile dust particles are observed to play characteristic role in the formation of dust ion-acoustic (DIA) compressive and rarefactive relativistic solitons in this plasma model. The critical value of the electron streaming ( $v_{e0})_{\mathrm{ crit}}$ in the process of generating solitary waves in this relativistic dusty plasma is shown to lie in the vicinity of the point/points, where $v_{e0} \approx v_{i0}$ . Further, the existence of compressive (rarefactive) solitons of much higher amplitudes is reflected in the immediate left (right) of this critical value ( $v_{e0})_{\mathrm{ crit}}$ within a short span of interval. Otherwise, the interval of existence of high-amplitude DIA compressive and rarefactive relativistic solitons is found to coincide with the assigned parametric domain of ion’s initial streaming ( $v_{i0})$ within the vicinity of electron’s ( $v_{e0}$ ’s) critical values. Moreover, the existence of critical range of $v_{i0}$ in a much lower domain suggests that the role of the massive ions in the presence of dust particles in the plasma is found predominant. A definite existence interval of $v_{i0}$ can be predicted for the generation of only DIA compressive relativistic solitons corresponding to every negligible value of $v_{e0}$ and large $Z_{d}$ in this model of dusty plasma. The high impact from the massive increase of negative charges $Z_{d}$ causes the extinction of compressive solitons at some upper limit of $v_{io}$ to earmark the interval of existence corresponding to each $Z_{d}$ .