Planar and Nonplanar Solitons in Multi-Ion Dusty Plasma

A rigorous theoretical investigation has been made on nonlinear dust-ion-acoustic (DIA) solitary waves (SWs) in a multi-ion dusty plasma system, consisting of inertial positive and negative ions, and arbitrary charged stationary dust. The dust particles have been considered as arbitrarily (either positively or negatively) charged in order to observe the effects of dust polarity on the DIA SWs. Three different approaches (K-dV (Korteweg-de Vries), mK-dV (mixed K-dV), and Gardner) have been employed to analysis the entire regime. The reductive perturbation method has been employed in all these three approaches. Using reductive perturbation method, we first derive K-dV equation which let us to analyze both types (bright and dark) of solitons, but, in a very limited region. After that mK-dV equation has been derived which let us analyze bright soliton for a large region, but cannot show the dark soliton. Finally, we have derived the Gardner equation employing the same method, through which we were able to analyze both the bright and dark solitons for a large region. We also employed the modified Gardner (mG) equation to observe the effects of nonplanar geometry as well as time evolution of SWs. It has been found that both the positive and negative solitons depend on the ion number density of the ions, dust polarity, temperature, as well as time scale. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.