الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
By using the reductive perturbation theory for the hydrodynamic equations of two-temperature ions, isothermal electrons, and negatively charged dust particles, a Korteweg-de Vries (KdV) equation is derived for nonlinear dust acoustic waves. At critical density of low temperature ions, the KdV equation cannot describe the propagation of the nonlinear dust acoustic waves. Therefore, a modified KdV (mKdV) and an extended KdV (EKdV) equations are derived at the critical density and in the vicinity of the critical plasma composition, respectively. The solitary wave solution is obtained and the behavior of the pulse profile is studied. The nonlinear Schrödinger equation (NLSE) at small wave number is derived for the electrostatic potential amplitude, that associated with the propagation of the envelope wavepackets. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in different Saturn’s rings (i.e. E-ring, F-ring, and B-ring). Numerical analysis indicates that the plasma parameters of the E-ring cannot support the propagation of rogue waves, but the rogue waves exist only in B- and F-rings. The variation of the structural properties of the rogue waves with relevant plasma parameters is investigated, in particular 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.