Nonlinearly coupled Langmuir and dust-acoustic waves in a dusty plasma

The nonlinear propagation of coupled Langmuir and dust-acoustic waves in a multicomponent dusty plasma is considered. The coupled mode propagation is described by a Schrodinger-Boussinesq system, which reduces to the Schrodin ger-KdV system for unidirectional wave propagation. For stationary propagat ion, the coupled waves are governed by a generic Hamiltonian that is integr able in both sub- and the supersonic regimes of Mach number. Depending on t he parameter regimes, exact analytical solutions for the coupled waves havi ng single-, double- and triple-hump structures for the Langmuir field inten sity are obtained. The exact governing equations for large-amplitude waves are also derived, and are solved approximately. The existence conditions fo r large-amplitude localized solutions in the quasineutral limit are discuss ed.