Existence of dust ion acoustic solitary wave and double layer solution at M = Mc

Dust Ion Acoustic Solitary Structures at the Acoustic Speed in the Presence of Nonthermal Electrons and Isothermal Positrons

“…Again, in the present paper, if we consider p = 0 then we observe that the system supports PPSWs, NPSWs, NPDLs, NPSWs after the formation of NPDL and negative potential supersolitons at the acoustic speed. These results agree with the results of Das et al 25 , where they have considered a collisionless unmagnetized three component dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions and Cairns distributed nonthermal electrons to investigate the DIA solitary structures at the acoustic speed.…”

“…Now, in the present work, if we consider p = 0, i.e., the positron concentration in the system is zero, then the present plasma system reduces to the exactly same system of Das et al 25 Figure 8 is the existence domain with respect to µ at p = 0 when σ ie = 0.9. This existence domain is qualitatively same as the existence domain as given in figure 10 in the paper of Das et al 25 In figure 8 (see figure 16). Since, the existence of solitons after the formation of double layer confirms the existence of at least one sequence of supersolitons 20 , therefore, we can conclude that whenever there exists no positron in the system, it supports negative potential supersolitons at the acoustic speed.…”

“…Again, since there does not exist any soliton after the formation of NPDL at the acoustic speed, there does not exist any negative potential supersoliton at the acoustic speed for p > 0. But for p = 0, i.e., if there is no positrons in the system, Das et al 25 found the existence of NPDLs and most importantly, the existence of negative potential supersolitons at the acoustic speed. Now, in the present work, if we consider p = 0, i.e., the positron concentration in the system is zero, then the present plasma system reduces to the exactly same system of Das et al 25 Figure 8 is the existence domain with respect to µ at p = 0 when σ ie = 0.9.…”

“…But for p = 0, i.e., if there is no positrons in the system, Das et al 25 found the existence of NPDLs and most importantly, the existence of negative potential supersolitons at the acoustic speed. Now, in the present work, if we consider p = 0, i.e., the positron concentration in the system is zero, then the present plasma system reduces to the exactly same system of Das et al 25 Figure 8 is the existence domain with respect to µ at p = 0 when σ ie = 0.9. This existence domain is qualitatively same as the existence domain as given in figure 10 in the paper of Das et al 25 In figure 8 (see figure 16).…”

“…Das et al 24 investigated dust acoustic (DA) solitary structures at the acoustic speed with the help of analytical theory developed in the same paper and they also prescribed a computational scheme to investigate the nature of existence of solitary structures at the acoustic speed. Later, Das et al 25 investigated DIA solitary structures at the acoustic speed in a collisionless unmagnetized dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions and Cairns distributed nonthermal electrons. They found that the system supports the negative potential solitary waves (NPSWs), positive potential solitary waves, negative potential double layers (NPDLs) and negative potential supersolitons at the acoustic speed.…”