Weak Relativistic Effect in the Formation of Ion-Acoustic Solitary Waves in Dusty Plasma

Role of streaming speeds of ions ( $u_{i0}$ ) and relativistic electrons ( $u_{e0}$ ) together with the immobile dust charge ( $Z_{d}$ ) to form dust-ion acoustic (IA) compressive and rarefactive relativistic solitons in this multispecies plasma model for immobile dusty plasma are investigated. In this new investigation of dust-IA waves with positive ions and relativistic electrons in presence of immobile dust, it is noteworthy to mention that only compressive Korteweg-de Vries (KdV) solitons are seen to produce for some pairs of initial streaming of ions and relativistic electrons. Whereas for some other pairs of ion and relativistic electron streaming speeds, rarefactive solitons of either increasing or decreasing character are seen to produce. The presence of dust charge of immobile dust, present in the plasma, plays a very crucial role to form compressive and rarefactive KdV solitons which is a salient feature of this theoretical investigation. The presence of massive dust particles in the stationary background of the plasma, andthe lighter ions and relativistic electrons get appreciable initial drifts which makes a great change in the growth of solitons which is a salient feature of this new investigation. The results of this finding may be great useful in space plasma and applications of this plasma model in space plasmas are also discussed in brief.