Dynamical properties of nonlinear dust ion-acoustic waves on the basis of the Schamel–KdV equation

In this present study, our objective is to investigate the formation of dust ion-acoustic solitary and periodic waves in a superthermal magnetised plasma featuring both positive and negative charged ions, energetic trapped electrons, and oppositely charged dust particles. We have used the reductive perturbation technique (RPT) to get the Schamel–Korteweg-de Vries (Schamel–KdV) equation, which describes the behaviour of dust ion-acoustic solitary waves (DIASWs). Based on the theory of planar dynamical systems, the possible existing solution of the Schamel–KdV equation is shown in the phase portrait diagram. Sagdeev’s pseudopotential equation is also derived and the features of DIASWs are analysed in combination with the soliton solution. Through the graphical presentation, we have analysed the role of the physical parameters on the characteristics of solitonic and periodic waves, along with the electric field. This investigation has the potential to elucidate the formation of nonlinear waves in diverse astrophysical settings (e.g., ionosphere, solar wind, mesosphere, auroral zone, magnetosphere, etc.) and also laboratory devices that contain opposite-polarity dust-charged particles, superthermally trapped electrons, and both positive and negative ion species.