Solitary waves in a dusty plasma with charge fluctuation and dust size distribution and vortex like ion distribution

A modified KdV equation is derived for the propagation of non-linear waves in a dusty plasma, containing N different dust grains with a size distribution and charge fluctuation with electrons in the background. The ions are assumed to obey a vortex like distribution due to their non-isothermal nature. The standard distribution for the dust size is a power law. The variation of the soliton width is studied with respect to normalized size of the dust grains. A numerical solution of the equation is done by considering the soliton solution of the modified KdV as the initial pulse. It shows considerable broadening of the pulse variation of width with β1 is shown.