Inherent Study of the Measures of Perturbation to Generate mKdV Solitons in Dusty Plasma with Relativistic Effects in Electrons and Ions

Abstract

The determination of the amplitudes of relativistic mKdV solitons based on specific amount of perturbation is presented for the first time in model of dusty plasma. The extremely high electrons’ streaming speed ${{v}_{{e0}}}$ is shown to enforce resultant relativistic speed of the bulk of plasma which necessitates smaller amount of perturbation to deal with the relativistic situation. Further, the increase in dust charge ${{Z}_{d}}$ is shown to diminish the amplitudes of mKdV solitons ($\phi _{0}^{'}$) for both cases of relativistic and non-relativistic solitons. Also, the high relativistic electrons’ streaming is found to serve as booster against small dust charge ${{Z}_{d}}$ to grow the amplitudes of mKdV solitons. On the other hand, higher streaming of the massive ions supplemented by small perturbation appears to dominate the growth of amplitude of mKdV solitons for both the cases.