Linear and nonlinear dust-hydromagnetic waves

A self-consistent and complete theory for linear, weakly nonlinear, and highly nonlinear dust-hydromagnetic waves in a magnetized dust-ion plasma has been presented. Oblique propagation as well as two typical special cases, propagation along and across the ambient magnetic field direction, are considered. The linear dispersion properties are analyzed by using the normal mode analysis. The weakly nonlinear properties are studied by employing the reductive perturbation method, which is valid for small but finite amplitude waves. The highly nonlinear properties are investigated by means of a pseudopotential approach, which is valid for arbitrary amplitude waves. The implications of our results to some space and astrophysical dusty plasmas are briefly mentioned