Dust ion acoustic solitons in a complex dusty plasma system with an adiabatic state

In this theoretical work nonlinear behavior of dust ion acoustic solitary waves (SWs) has been investigated, and then the effect of the adiabatic change on them has been observed. The complex plasma system consists of inertial positive and negative ions, Maxwell's electrons, and positively and negatively charged stationary dust particles. The effects of dust polarity on the dust ion acoustic SWs have also been observed. Using the reductive perturbation method, we first derive K-dV equation which lets to analyze both the positive (bright) and negative (dark) solitons in a very limited region. After that mK-dV equation has been derived, and this let to analyze positive soliton for a large region, but cannot show the negative soliton. Finally, the Gardner equation has been derived employing the same method, through which we were able to analyze both the positive and negative solitons for a large region. It has been found that both the positive and negative solitons significantly depend on the mass number density, ion number density, and dust polarity in the adiabatic and isothermal system.