Propagation of shock structures in inhomogeneous dusty plasmas with dust size distribution and nonadiabatic dust charge fluctuation

Propagation of nonlinear shock structures in inhomogeneous dusty plasmas with power law dust size distribution and nonadiabatic dust charge fluctuation has been investigated. Using reductive perturbation expansion, the hydrodynamic equations are reduced to a modified variable coefficient Korteweg–de Vries (MKdV)–Burgers equation governing the characteristic of shock structures. Two different types of shock structures exist in this system and transform each other. The numerical results show that the inhomogeneity, the power law dust size distribution and the nonadiabatic dust charge fluctuation have strong influence on the nonlinear properties of shock structures and the transition condition between monotone shock structures and oscillatory shock structures.