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    Öğe
    Breather, lump, M-shape and other interaction for the Poisson-Nernst-Planck equation in biological membranes
    (Springer, 2024) Ceesay, Baboucarr; Ahmed, Nauman; Baber, Muhammad Zafarullah; Akguel, Ali
    This paper investigates a novel method for exploring soliton behavior in ion transport across biological membranes. This study uses the Hirota bilinear transformation technique together with the Poisson-Nernst-Planck equation. A thorough grasp of ion transport dynamics is crucial in many different scientific fields since biological membranes are important in controlling the movement of ions within cells. By extending the standard equation, the suggested methodology offers a more thorough framework for examining ion transport processes. We examine a variety of ion-acoustic wave structures using the Hirota bilinear transformation technique. The different forms of solitons are obtained including breather waves, lump waves, mixed-type waves, periodic cross-kink waves, M-shaped rational waves, M-shaped rational wave solutions with one kink, and M-shaped rational waves with two kinks. It is evident from these numerous wave shapes that ion transport inside biological membranes is highly relevant, and they provide important insights that may have an impact on various scientific disciplines, medication development, and other areas. This extensive approach helps scholars dig deeper into the complexity of ion transport, illuminating the complicated mechanisms driving this essential biological function. Additionally, to show the physical interpretations of these solutions we construct the 3D and their corresponding contour plots by choosing the different values of constants. So, these solutions give us the better physical behaviors.
  • [ X ]
    Öğe
    Modelling Symmetric Ion-Acoustic Wave Structures for the BBMPB Equation in Fluid Ions Using Hirota's Bilinear Technique
    (Mdpi, 2023) Ceesay, Baboucarr; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akgül, Ali; Cordero, Alicia; Torregrosa, Juan R.
    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 find solutions and predict the behaviour 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 behaviour of the solutions, some 3D plots and their respective contour level are shown, choosing different values of the parameters.