Nonlinear Alfvén waves in magnetized plasmas with heavy impurities or dust

Nonlinear electromagnetic wave propagation in a magnetized plasma with heavy impurities, in particular, dust grains, at frequencies below and of the order of the ion-cyclotron frequency is considered. The presence of immobile dust grains leads to a considerable change of the dispersion characteristics for Alfv\'en waves propagating along the uniform magnetic field, especially for small wave numbers when two modes with a relatively large frequency gap appear. We discuss the consequences of this dispersion for the nonlinear properties of the waves.