Nonlinear instabilities in a dusty plasma sheath

The nonlinear coupling between large amplitude ion waves and dust-acoustic waves (DAWs), as well as dust-lattice waves (DLWs), in a dusty plasma sheath is considered. By employing a two-fluid approach, we derive a system of coupled equations for the ion waves and the DAWs/DLWs; the latter are nonlinearly driven by the ion wave ponderomotive force. A normal mode analysis of our nonlinearly coupled equations is performed to obtain general dispersion relations that are useful for studying modulational instabilities. The implications to laboratory plasmas are pointed out.