Collective nonlinear dust–plasma interactions

New aspects of collective nonlinear dust–plasma interactions are presented. These are the formation of dust ion-acoustic shocks and Langmuir envelope solitons in a uniform dusty plasma, as well as self-organization of incompressible dust fluid in the form of vortical structures in a non-uniform dusty plasma. We present relevant non-linear models and their numerical simulations for those nonlinear waves and structures. The relevance of our investigation to laboratory and space dusty plasmas is discussed.