Effects Of Relative Strength Of Dispersion On The Formation Of Nonlinear Waves In Dusty Plasmas

In this paper, we studied the effect of strength of dispersion on the formation of solitons and shock waves in un-magnetized dusty plasma using the reductive perturbative technique. Different relational forms of strength parameter ε were chosen such a way that it altered the stretching of space, x and time, t variables, thereby leading to different nonlinearities. First, we considered the form ζ = √(ε(x-v0t)) and τ = √(εt), where v0 is the phase velocity, with 0<ε<1 is the parameter that measures the strength of the dispersion. We obtained the Korteweg-de Vries (KdV) equation for un-modulated dust acoustic wave with solitary wave-type solution. The effect of dissipation on the wave propagation was analyzed with coordinate transformations ζ ε(x-v0t) and τ = ε2t, with 0<ε<1. This led to Burgers' equation with shock wave-type solution. From this study, we concluded that when the dissipation effect is negligible in comparison with dispersion, dust charge fluctuations can only change the amplitude of solitary wave, as observed in the KdV case. However, when the system is not sufficiently dispersive, the dissipation due to dust charge fluctuations can play dominant role and eventually leads to the formation of dust-acoustic shock wave.