Modelling the Symmetric Wave Structures of the Ion-Acoustic for the BBMPB Equation in the Fluid Ions Using Hirota Bilinear Technique

This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The various types of wave structures, are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately solutions and predict the behavior of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behavior of the solutions, some 3D plots have been performed and their respective contour level, choosing different values of the parameters.