A nonlinear Zakharov-Kuznetsov equation in magnetized dusty plasmas with dust charge fluctuation and dust size distribution

By using the reductive perturbation method, a nonlinear Zakharov-Kuznetsov equation governing the dust acoustic (DA) solitary waves is derived for magnetized dusty plasmas which contains N different dust grains with a size distribution and charge fluctuation, nonthermally distributed ions and Boltzmann distributed electrons. We analyse the effects of dust charge fluctuation, the temperatures of dust grains and ions, and dust size distribution on the natures of the DA solitary waves.