Applied Mathematics & Information Sciences

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The release of rogons (rogue waves) associated with the electrostatic perturbations in dusty plasmas containing twotemperature ions is investigated. Solving the fluid equations using perturbation method, a nonlinear Schr¨odinger equation (NLSE) is derived for the electrostatic potential amplitude, associated with the propagation of envelope wavepackets. The solution of the NLSE is presented, which proposed as an effective tool for studying the rogons in different Saturn’s rings (i.e. E-ring, F-ring, and B-ring). Our analysis indicates that the plasma parameters of the E-ring cannot support the propagation of rogue waves, but the rogue waves may exist in B- and F-rings. The existence region of the created rogons is defined, as well as the forbidden zone of rogue waves is examined. The variation of the structural properties of the rogons with relevant plasma parameters is investigated, in particular focusing on the ratio between the low-temperature ion number density-to-dust number density, as well as the temperature ratio between the low-temperature ions-to-electrons.

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