Effect of Trapping of Heavy Negative Ions on the Evolution of Shock Wave in a Dust Charge Fluctuating Plasma: A Trapped K-dV-Burgers’ Equation

We have investigated the propagation characteristics of small-amplitude electrostatics shock waves in an unmagnetized dusty plasma in the presence of positive and negative dust charge fluctuation with trapped negative ions. Here, we have derived the evolution equations for dust acoustic shock waves in the form of trapped Burgers' (T-Burgers') equation and trapped Korteweg-de Vries-Burgers' (T-K-dV-Burgers') equation with the help of the standard reductive perturbative technique. The present plasma system supports both the regime of nonlinear waves propagation, i.e., subsonic and supersonic. It is noticed that the temperature ratio of both positive and negative ions has extensive control of the maximum amplitude of the shock wave propagation. Also, it is found that, due to the dispersive and dissipative forces, the shock waves governed by the T-K-dV-Burgers' equation are better localized than the shock waves governed by the T-Burgers' equation. It is also worth mentioning to note that nonlinearity plays a vital role in controlling the maximum amplitude of the shock wave when it is governed by the T-Burgers' equation, whereas both nonlinearity and dissipation play a leading role in controlling the maximum amplitude of the shock waves when it is governed by the T-K-dV-Burgers' equation.