Envelope solitons and rogue waves in Jupiter's magnetosphere

Considering a system of positively charged different sizes of dust grains which interacts with streaming electrons and ions, modulational instability (MI) together with the formation of envelope solitons and rogue waves are studied in Jupiter's middle magnetosphere. A nonlinear Schrodinger equation (NLSE) is derived and three distinct wave modes are observed among which the slowest mode is significantly affected by power law dust size distribution (DSD). For this mode, DSD enhances the MI growth rate in the unstable domain. The effects of densities of streaming electron and ion beams on the instability and different characteristics of the envelope solitons are investigated. How the number densities of electron and ion beams influence the spatiotemporal evolution of the associated rogue waves are also discussed.