Transverse Perturbations on Dust Acoustic Solitary Waves with Vortex-Like Ion Distribution in Two-Dimensional Cylindrical Geometry

Nonlinear dust acoustic solitary waves (DASWs) in an unmagnetized dusty plasma with a negatively charged dust fluid are studied in bounded two-dimensional (2D) cylindrical geometry. The dusty plasma was assumed to have electrons with Boltzmann distribution and ions with vortex-like distribution. Transverse perturbation was observed in such dusty plasma. By using the reductive perturbation method along with new space-time stretched coordinates, modified Korteweg–de Vries (K–dV) equation was derived for cylindrical geometry. Particularly, exact solution for the modified K–dV equation in 2D cylindrical geometry was obtained. The solution was investigated for different physical parameters of the plasma. It has been found that the trapped ions have significant effect on the properties of nonlinear waves (small but finite amplitude and width) in cylindrical geometry. The results also show that only compressive solitary waves can be formed in this system. According to the results, the properties of the DASWs in 2D cylindrical geometry differ from 1D cylindrical geometry. Furthermore, unlike the planar modified K–dV equation, in cylindrical modified K–dV equation, solitary structures are slightly deformed in time. The results of present investigation may help to understand the nature of DA solitary structures where dust along with non-Maxwellian ions exists. Such structures can be found in different regions of space and astrophysics mediums.