Nonplanar ion acoustic waves in dusty plasma with two temperature electrons: Application to Saturn's E ring

In the present paper, we have studied the cylindrical/spherical ion acoustic waves in dusty plasma consisting of positive ions, immobile dust particles, and q nonextensive distributed cold and hot electrons. A multiple scale expansion method is employed to derive a modified Korteweg–de Vries (mKdV) equation. Exact analytical solution for the mKdV equation in nonplanar geometry is obtained using the weighted residual method. This solution is, then, plotted for different physical parameters relevant to Saturn's E ring through 2D figures. We show that the amplitude of the wave decreases faster as one departs away from the axis of the cylinder or the center of the sphere. Such a decaying behavior continues as time progresses. This is expected from the obtained solution where the cylindrical (spherical) amplitude component $(τ∞/τ)m$ decreases as the time progresses. We have also studied the role of the nonadiabatic dust charging fluctuating dissipation process and analyzed the resulting damped mKdV equation. Furthermore, the parametric dependence of wave properties (amplitude and width) on the q nonextensive parameter, density, and temperature of cold and hot electrons, concentration of dust particles, and thermal effects of ions has been studied in detail, and findings obtained here will be beneficial to further astrophysical investigations.