Abstract
A theoretical work has done to observe the existence of dust ion-acoustic (DIA) solitary waves (SWs) in a multi-ion dusty plasma system consisting of inertial positive and negative ions, Maxwell’s electrons, and arbitrary charged stationary dust. In this short communication, our research declares that with these components the derivation of Korteweg-de Vries (K-dV) and mixed K-dV (mK-dV) is possible. Here reductive perturbation method has been employed in all these approaches. The first K-dV equation has been derived which gave both bright and dark solitons but for a very limited region. Then the mK-dV equation has been derived that gave bright soliton for a large region, but no dark soliton has been observed.

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