The 3+1 dimensional Kadomtsev?Petviashvili Burgers' equation in non-uniform dusty plasmas

Using the perturbation method, the 3+1 dimensional modified variable coefficient Kadomtsev–Petviashvili (MKP) Burgers' equation governing nonlinear dust acoustic shock waves is derived with the combined effects of non-adiabatic dust charge fluctuation, higher-order transverse perturbation and the non-thermally distributed ions in inhomogeneous dusty plasmas due to spatial gradients of dust charge and plasma densities for the first time. The MKP Burgers' equation is reduced to the standard variable coefficient Kadomtsev–Petviashvili (KP) Burgers' equation. A particular solution of this KP Burgers' equation is also obtained. It is shown that the dust acoustic shock waves can exist in the KP Burgers' equation.