Inherent Study of the Measures of Perturbation to Generate mKdV Solitons in Dusty Plasma with Relativistic Effects in El
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Inherent Study of the Measures of Perturbation to Generate mKdV Solitons in Dusty Plasma with Relativistic Effects in Electrons and Ions B. C. Kalitaa, b, * and D. Bhattacharjeeb, ** a Cotton
b
University, Guwahati, Assam, 781001 India Department of Mathematics, Gauhati University, Guwahati, Assam, 781014 India *e-mail: [email protected] **e-mail: [email protected] Received April 11, 2019; revised January 12, 2020; accepted February 18, 2020
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 ve0 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 (φ'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. Keywords: solitons, dusty plasma, modified Korteweg–de Vries equation DOI: 10.1134/S1063780X20100050
1. INTRODUCTION The fascinating space laboratory is a beautiful granary of nonlinear phenomena generated by magnetized and unmagnetized plasmas with the partial supports of radiation, solar flares and planetary dusts. In the regions like ionosphere, magnetosphere and interplanetary space, the nonlinear behavior of plasmas is found to change in a variety of ways. Out of the nonlinear waves, solitary waves (solitons) are a peculiar kind of waves in plasmas of special character. They have been studied in extensive detail (not reported here) for the last five decades. Still, abundant scopes are left to investigate due to the emergence of dust particles, relativistic effects, quantum effects, non-thermal and super thermal particles in the plasma systems. The studies of nonlinear waves in any media are pursued in general as means of continuum hypothesis under the crude assumption that it is discrete. This idea can rightly be substantiated with the help of representative waves given by the modified Korteweg–de Vries (mKdV) equation considering the absence of nonlinearity of the corresponding wave generated by the Korteweg–de Vries equation. The modified KdV equation is derived [1] to establish different kinds of nonlinear waves called mKdVsolitons in plasma. But with the time, it has become a
fertile area of research with the increase of feasible number of components within the plasma. The presence of dust particles in interplanetary space and various dynamical effects in the behavior of plasma particles in space make the situation more fascinating. Theoretically, ion acoustic waves (IAW) were studied with the appli
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