Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

Abstract

The nonlinear dust-ion-acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns-Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z-axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov-Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg-de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non-thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non-thermal electrons, pair-ions, and dust particles can exist. KEYWORDSdust-ion-acoustic solitary wave, the bifurcation theory, the Cairns-Gurevich distribution, the modified Zakharov-Kuznetsov equation, the reductive perturbation technique

Bifurcation types and dynamic control of dust ion‐acoustic waves propagation in dusty plasmas with non‐thermal electrons

“…They showed that non‐extensivity parameter and dust concentration play a crucial role in the evolution of non‐linear and super‐nonlinear DIA waves. Abdikian [ 32 ] investigated DIA solitary waves in a magnetized dusty pair‐ion plasma with opposite polarity of dust grains, and showed the effects of plasma parameters on the existence of solitary waves through the phase portraits analysis of the dynamical system.…”

Effects of trapped ions concentration on the dynamics of dust‐acoustic periodic travelling waves in dusty plasmas

“…Singh et al [ 29 ] illustrated that the amplitude and the width of negative potential DA soliton profiles increase with the decrease in polarization force. Abdikian [ 30 ] examined the non‐linear behaviour of dust‐ion‐acoustic solitary structures in a dusty plasma, including both negative and positive ions with the Cairns‐Gurevich distribution for electrons and immobile opposite polarity dust particles. Abdikian [ 30 ] illustrated that dust‐ion‐acoustic soliton energy increases with the increase of the trapping parameter for electrons.…”

“…Abdikian [ 30 ] examined the non‐linear behaviour of dust‐ion‐acoustic solitary structures in a dusty plasma, including both negative and positive ions with the Cairns‐Gurevich distribution for electrons and immobile opposite polarity dust particles. Abdikian [ 30 ] illustrated that dust‐ion‐acoustic soliton energy increases with the increase of the trapping parameter for electrons. Recently, Demiray and Abdikian [ 31 ] applied the non‐linear field equations of hot dusty plasma in the presence of nonthermal electrons and trapped ions.…”

Bifurcation analysis of ion-acoustic waves in an adiabatic trapped electron and warm ion plasma

“…Many researchers have tried to find effects of trapped particles in plasma on the genesis and propagation of solitary wave features [38][39][40]. Very recently, by applying the RPT and hydrodynamic model equations for the ion fluid, Abdikian [41] has studied the nonlinear DIA solitary waves in magnetized dusty plasmas with negative and positive ions, and stationary opposite polarity dust particles. By considering the Cairns-Gurevich distribution for electrons, the author has derived the modified ZK equation and discussed how the different plasma parameters have an influence on the solitary wave features.…”