Dust-acoustic modulated structures in self-gravitating magnetized electron depleted dusty plasmas: multi-rogue waves and dark soliton collisions

A theoretical model has been developed to study the effects of the gravitational attraction and magnetic field on the waves instabilities as well as the dynamics of dust-acoustic rogue waves (RWs) and the collisions of the envelope dark soliton in self-gravitating non-Maxwellian magnetized electron depleted dusty plasma (EDDP). Using the derivative expansion method, the basic fluid equations of the model are converted to the normal nonlinear Schrödinger equation (NLSE). The modulational instability (MI) analysis is used for determining the regions of (un)stable envelope structures (RWs and envelope solitons). According to gravitational force, a new dispersion relation is obtained and analyzed numerically. It is noted that the presence of gravitational force provides the possibility of a novel purely growing instability mode. Effects of gravitational force and magnetic field on the growth rate of MI and the profile of the RWs in unstable regions and on the phase shifts of the colliding dark solitons in stable regions are discussed in detail. In general, the gravitational force leads to destabilized waves whereas the magnetic field plays the stabilizing role. The present investigation may be of relevance for understanding the mechanism which govern the formation and propagation of modulated DA structures (RWs and envelope solitons) in certain astrophysical objects such as Saturn rings, interstellar medium, dark interstellar clouds, HI and HII regions of galaxies.