The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dustgrains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.
Volume 94, 2020
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