This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON PLASMA SCIENCE 1 Weakly Relativistic Ion-Acoustic Solitary Waves in Dusty Plasma B. C. Kalita and Samiran Das Abstract— The streaming speeds of relativistic electrons (v e0 ) and ions (v i 0 ) 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 ) 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 ≈ v i 0 . Further, the existence of compressive (rarefactive) solitons of much higher amplitudes is reflected in the immediate left (right) of this critical value (v e0 ) 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 i 0 ) within the vicinity of electron’s (v e0 ’s) critical values. Moreover, the existence of critical range of v i 0 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 i 0 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 . Index Terms— Dust charges, dusty plasma, relativistic solitons. I. I NTRODUCTION T HE study of nonlinear phenomena in various media is of immense growing interest among the researchers of the world. The complexity of such type of phenomena which cannot be easily dealt is the main cause to attract researchers. Space is an interesting laboratory for fascinating structures of plasma. Solitary waves of various categories in plasmas, detected by means of different space probes, are peculiar kind of nonlinear waves. Investigation of ion-acoustic (IA) solitary waves in the presence of usual two and multicomponent plasmas has been undertaken extensively in the last few decades (its report is beyond the scope of this paper). The introduction of relativistic effects and quantum effects in the formation of solitary waves is a recent trend of research. Besides, the presence of (charged) dust particles in plasma is Manuscript received February 6, 2017; revised August 14, 2017; accepted August 22, 2017. The review of this paper was arranged by Senior Editor T. Hyde. (Corresponding author: Samiran Das.) B. C. Kalita is with the Department of Mathematics, Gauhati University, Guwahati 781014, India. S. Das is with the Department of Basic Sciences (Mathematics), Central Institute of Technology, Kokrajhar 783370, India (e-mail: s.das@cit.ac.in). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2017.2749452 found to drastically change the properties of solitary wave structures both in space and laboratory plasmas. In addi- tion to theoretical importance, applications observed in earth’s magnetosphere [1] and cometary tails [2], [3] in the neighborhood of stars [4], planetary rings [5], and asteroid zones make the study of space phenomena in dusty plasma more attractive at the present time. Much information has been furnished [6] about dusty plasmas of interstellar clouds. Whipple et al. [7] and Angelis et al. [8] have observed creation of spatial inhomogeneity for the distribution of immo- bile dust particles, and it has projected modification [9] of wave spectra for static dust particles in plasmas. Again, the generation of extremely low-frequency dust acoustic (DA) waves in unmagnetized plasmas is also studied [10]. The existences of linear and nonlinear DA waves and dust IA (DIA) waves have been experimentally observed by Angelo [11] and Duan et al. [12]. In unmagnetized dusty plasma, large-amplitude rarefactive and compressive solitons in plasma with nonthermal ion distributions and vortex-like effect have also been studied [14]. Also, in a low-temperature dusty plasma similar to those in laboratory and space environ- ments, the existence of rarefactive solitary waves is reported by Mamun et al. [15]. DIA waves at high frequency in planetary rings [16] and also at low frequency are established [17]–[20] in dusty plasmas under various compositions. Verheest and Pillay [21] have shown the existence of solitons with pos- itive and negative potentials confined to some parametric domains. Using perturbation method, DA solitary waves through Zakharov–Kuznetsov equation is also studied [22]. It is found to investigate DA solitary waves with nonthermal ion distributions in plasmas by means of energy integral [23]. Ironically, in dusty plasma, Kundu et al. [24] have established rarefactive solitons but in magnetized plasmas. In all these investigations, relativistic effects are not incor- porated in the formation of DA and DIA solitary waves in plasmas. Inclusion of relativistic effects in IA waves with- out dust particles has been taken into account by Chat- tarjee and Roychoudhury [25], Roychoudhury et al. [26], Singh et al. [27], Gill et al. [28], Hasegawa et al. [29], and Kalita and Deka [30]. Interestingly, Kalita and Deka [31], in their recent investigation, have established existence of both compressive and rarefactive relativistic solitons in a plasma with adiabatic electrons and isothermal ions subject to a new valid condition. The effects of positively and negatively charged dust parti- cles on the formation of IA solitary waves in fully relativistic dusty plasma are seen to investigate [2] on the basis of 0093-3813 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.