The effect of dust size distribution for vortex-like ion distribution dusty plasma

A reasonable normalization for vortex-like ion distribution dusty plasma with many different dust grains is adopted. For this system with N different dust grains, we have derived a modified Korteweg-de Vries equation for small, but finite amplitude dust acoustic waves. We have also studied the case that the dust grains satisfy the power law distribution and the ions satisfy the vortex-like ion distribution, and found that the soliton velocity is larger than that of mono-sized dusty plasma with average dust size of power law distribution. We have studied the amplitude and the width of a soliton existing in a dusty plasma as well, and concluded that if one soliton exists in a dusty plasma with power law distribution the smaller grains have larger velocities and propagate longer distances than that of larger grains. (C) 2003 Published by Elsevier B.V.