Kadomtsev-Petviashvili (KP) Burgers equation in dusty negative ion   plasmas: Evolution of dust-ion acoustic shocks
  We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves. 
A. N. Dev, J. Sarmah, M. K. Deka, A. P. Misra and N. C. Adhikary
physics.plasm-ph