Dust ion acoustic (DIA) solitons in an unmagnetized pair-ion (PI) plasmas with adiabatic pair-ions, non-isothermal electrons, and negatively charged background dust are investigated, using both small and arbitrary amplitude techniques. An energy integral equation involving the Sagdeev potential is derived, and basic properties of the large amplitude solitary structures are investigated. The effects of dust concentration, resonant electrons, and ion temperatures on the profiles of the Sagdeev potential and corresponding solitary waves are studied. The related Schamel-Korteweg-de Vries (S-KdV) equation with mixed-nonlinearity is derived by expanding the Sagdeev potential. Asymptotic solutions for different orders of nonlinearity are discussed for DIA solitary waves. The present work is applicable to understand the wave phenomena and associated nonlinear electrostatic perturbations in the doped pair ion plasmas, not completely filtered e.g., pair ion-electron plasmas, enriched with an extra massive charged component (e.g., dust defects), which may be academic for the moment but might be of interest for forthcoming experiments in laboratory (space) plasmas.

The pressure effect on the small amplitude solitary waves in a complex superthermal plasma composed of electrons, ions and dust is discussed. The Korteweg-de-Vries (KdV) equation and its model solution are derived using standard reduction perturbation techniques. Pressure is shown to significantly affects the existing mode in a superthermal environment. The imperative role is played here by the spectral index κ and the dust charge that strongly affect the properties of the nonlinear structures. The results obtained are compared with those acquired by the homotopy perturbation method (HPM). We see a strong correlation in the small time limit with our analytical calculations and those obtained by the HPM technique.

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