A theoretical work has been made on the nonlinear propagation of dust ion acoustic (DIA) solitary waves (SWs) and double Layers (DL’s) in a multi-ion dusty plasma system (MIDP), consisting of inertial positive and negative ions, Maxwell’s electrons, 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 and DL’s. The basic properties and dynamics of planar solitary waves (SWs) and double layers (DLs) have been observed. Through this work the changing of basic properties of these waves with thermal states have also been observed. First, a detail mathematical derivation and numerical analysis on the linear properties as well as the dispersion relation in the dusty multi-ion system at isothermal system has done. Then in order to observe the nonlinear properties through the entire regime, three different approaches (K-dV (Korteweg-de Vries), mK-dV (mixed K-dV), and Gardner) have been employed for both the isothermal and adiabatic systems. The reductive perturbation method has been employed in all these three approaches. Using reductive perturbation method, we ﬁrst derive K-dV equation which let to analyze both bright and dark solitons in a very limited region. After that mK-dV equation has been derived which let analyze bright soliton for a large region, but cannot show the dark soliton and DL’s. Finally, Gardner equation has been derived employing the same method, through which we were able to analyze both the bright and dark solitons for a large region. .
Received: May 2018
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