Abstract
A theoretical investigation has been made on the nonplanar (cylindrical and spherical) dust-ion-acoustic (DIA) double layers (DLs) in a dusty plasma system, containing inertial ions, Boltzmann electrons, and negatively charged stationary dust. In this investigation, in order to analyze the time dependent nonplanar DIA DLs, we have used the modified Gardner equation, which has been obtained by employing the reductive perturbation method. It has been found that the behaviors of DIA DLs have been significantly modified by the time period and the nonplanar geometry. The nonplanar DIA DLs has been found to be similar with planar DIA DLs only at large time scale and the cylindrical DIA DLs have been found to be smaller than the spherical DLs, but larger than the planar DLs.
Highlights
The existence of novel dust-ion-acoustic (DIA) waves was first predicted by Shukla and Silin [1] about twenty years ago
The nonplanar DIA double layers (DLs) has been found to be similar with planar DIA DLs only at large time scale and the cylindrical DIA DLs have been found to be smaller than the spherical DLs, but larger than the planar DLs
DLs are bounded by the lower and upper surface plot of Figure 3, and DLs exist for parameters corresponding to any point in between two ( = 0 ) surface plots
Summary
The existence of novel dust-ion-acoustic (DIA) waves was first predicted by Shukla and Silin [1] about twenty years ago. In all of these investigations [29,30,31], authors have used the K-dV or Burgers equations, which are not valid for a parametric regime corresponding to A = 0 or A ~ 0 (where A is the coefficient of the nonlinear term of the K-dV or Burger equation [29,30,31], and A ~ 0 means here that A is not equal 0, but A is around 0) This is because, the latter gives rise to infinitely large amplitude structures which break down the validity of the reductive perturbation method [32]. In our present work we are going to analyze the nonplanar DIA DLs in dusty plasma system by deriving the modified Gardner (mG) equation
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