The effect of dust size distribution for two ion temperature dusty plasmas

A reasonable normalization for two ion temperature dusty plasmas with many different dust grains is adopted, which varies self-consistently with the system parameters. For this system with N different dust grains, we use the reductive perturbation technique and derive a Korteweg de Vries equation for small, but finite amplitude dust acoustic waves for both discontinuous dust size distribution and continuous power law distribution. We have found that if the dust grain sizes satisfy the power law distribution, the soliton velocity will be larger than that of mono-sized dusty plasmas with average dust size of power law distribution. The amplitude and the width of the soliton existing in the two ion temperature dusty plasmas have been discussed in this paper as well. We also found that if one soliton exists in a dusty plasmas with power law dust size distributions the smaller grains will have larger velocities and propagate longer distances than that of larger grains.