The contribution of electron inertia to the evolution of solitons in weakly and strongly inhomogeneous plasmas having streaming ions and electrons with weak relativistic effect is studied on the basis of a relevant Korteweg–de Vries equation derived with the help of reductive perturbation technique. Three types of modes (fast, medium, and slow) are found to propagate in the plasma. In case of weak (strong) inhomogeneous plasma, only the fast (slow) mode corresponds to the soliton evolution. For the propagation of solitons in strongly inhomogeneous plasma, there is no restriction on the ion and electron velocities but in case of weak inhomogeneity the solitons are possible only for a particular range of velocity difference. This range shows the dependence on the temperature and mass ratios of the ions and electrons. In addition, it is realized that only the rarefactive solitons are possible in the present plasma model. The effect of electron inertia on the phase velocity, peak soliton amplitude, and soliton width is studied together with the effects of plasma density, ion temperature, and speeds (relativistic effects) of ions and electrons.

One-dimensional evolution of solitons in a two-fluid plasma having weakly relativistic streaming ions and electrons is studied through usual Korteweg–de Vries equation under the effect of electron inertia. Although fast and slow ion acoustic modes are possible in such a plasma, only the fast mode corresponds to the soliton propagation for a particular range of velocity difference of ions and electrons. This range depends upon the ratios of mass and temperature of the ions and electrons. The effect of electron inertia on the propagation characteristics of the soliton is studied for typical values of the speed and temperature of the ions and electrons and it is found that this effect is dominant over the relativistic effect and the effect of ion temperature.

Main concerns of the present article are to investigate the effects of dust charging and trapped electrons on the solitary structures evolved in an inhomogeneous magnetized plasma. Such a plasma is found to support two types of waves, namely, fast wave and slow wave. Slow wave propagates in the plasma only when the wave propagation angle θ satisfies the condition θ≥tan-1{(1+2σ)-[(ndlh(γ1-1))/(1+ndlhγ1)]-v0u0}, where v0(u0) is the z- (x-) component of ion drift velocity, σ = Ti/Teff, ndlh = nd0/(nel0 + neh0), and γ1=-1Φi0[1-Φi01+σ(1-Φi0)] together with Ti as ion temperature, nel0(neh0) as the density of trapped (isothermal) electrons, Φi0 as the dust grain (density nd0) surface potential relative to zero plasma potential, and Teff=(nelo+neho)TelTeh/(neloTeh+nehoTel), where Tel(Teh) is the temperature of trapped (isothermal) electrons. Both the waves evolve in the form of density hill type structures in the plasma, confirming that these solitary structures are compressive in nature. These structures are found to attain higher amplitude when the charge on the dust grains is fluctuated (in comparison with the case of fixed charge) and also when the dust grains and trapped electrons are more in number; the same is the case with higher temperature of ions and electrons. Slow solitary structures show weak dependence on the dust concentration. Both types of structures are found to become narrower under the application of stronger magnetic field. With regard to the charging of dust grains, it is observed that the charge gets reduced for the higher trapped electron density and temperature of ions and electrons, and dust charging shows weak dependence on the ion temperature.

On the basis of appropriate modified KortewegdeVries (mKdV) equation derived for three cases of n n0 < n e0 , n n0 = n e0 , and n n0 > n e0 together with n n0 (n e0 ) as the density of negative ions (electrons), we observe that compressive and rarefactive mKdV solitons propagate in an inhomogeneous magnetized plasma having negative ions at their critical density. Two types of modes (fast and slow) separately evolve as the compressive and rarefactive solitons. However, only the solitons corresponding to the fast mode get reflected, if the obliqueness of the magnetic field lies under certain critical angle ψ CR which gets larger under higher thermal motions of the ions and shows stronger dependence on it when less number of negative ions are present in the plasma. There is a possibility of the change of polarities after the reflection of the solitons. The solitons suffer stronger reflection under the effect of larger ion thermal motions and smaller obliqueness of the magnetic field. The compressive solitons are found to downshift, whereas the rarefactive solitons are upshifted after the reflection, and these shifts get higher for the increasing concentration of the negative ions and lower obliqueness of the magnetic field. The compressive (rarefactive) solitons shift less (more) in the plasmas with ions of higher thermal energy; however, the upshift shows opposite behavior for the case of n n0 > n e0 .Index Terms-Compressive and rarefactive solitons, critical density, negative ions, soliton reflection, thermal and gyratory motions of ions.

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