Shock wave in one-dimensional dusty plasma crystal with charge gradient

In this paper, the effect of charge gradient in a one-dimensional dusty plasma crystal is considered to investigate shock structure. Under the continuum limit, the nonlinear Korteweg–de Vries (KdV)–Burgers equation with a charge gradient effect is derived using the reductive perturbation method. Then, the shock solution based on the KdV–Burgers equation is obtained. The influence of the parameter ε, which measures the effect of charge gradient on the dynamic of the shock wave, is discussed in detail. It is found that the shock amplitude and strength increase with the increase in the parameter ε. Furthermore, it is also found that charge gradient effect makes oscillatory shock more easily converted to monotonic shock.