Dust Alfven ordinary and cusp solitons and modulational instability in a self-gravitating magneto-radiative plasma

. The effective one-fluid adiabatic magnetohydrodynamic (MHD) equations for a multicomponent plasma comprising of electrons, ions, and dust are used to investigate the nonlinear coupling of dust Alfven and dust acoustic waves in the presence of radiation pressure as well as the Jean’s term that arises in a self-gravitating plasma. In this context, the set of Zakharov equations are derived. The soliton solutions in the presence of radiation pressure and Jeans term are separately discussed. It is found that ordinary solitons are obtained in the absence of Jeans term whereas cusp solitons are found in the absence of radiation pressure. To the best of our knowledge, cusp solitons are obtained for the first time for a self-gravitating plasma with Jeans term for an electromagnetic wave in a dusty plasma. The modulational instability is also investigated in the presence of radiation pressure and Jeans term. It is found that the Jeans term drives the system modulationally unstable provided it dominates the dust acoustic and radiation pressure terms whereas the radiation pressure enhances the stability of the system. The relevance of the present investigation in the photodissociation region that separates the HII region from the dense molecular clouds is also pointed out.