Multi-Wave, Breather, and Interaction Solutions to Akbota Equation for The Heisenberg Ferromagnet-Type Model Arising in Nonlinear Physical Sciences

This paper investigates the integrable Akbota equation, a Heisenberg ferromagnet-type model. It is a basic tool for understanding curve and surface geometry. The interactions between atoms’ magnetic moments are described by Heisenberg ferromagnetism. This equation is investigated utilizing the logarithmic transformation, the multi-wave technique, the homoclinic breather approach, and the interactional solution using the double exp-functions strategy. A well-known idea in nonlinear research, the multi-wave approach clarifies that three waves interact under particular resonance circumstances. A breather wave is a localized oscillatory solution that preserves its form as time progresses. Additionally, we will analyze the dynamics of the newly derived solutions through graphical representations, assigning suitable values to the parameters. The offered methods are clear and precise, making it possible to extend the established form to additional nonlinear models. In contrast to prior investigations in the literature, our results are noteworthy. These results could be significant for further exploration of such frameworks to address nonlinear issues in applied sciences. Furthermore, the results enhance our understanding of fluid propagation and incompressible fluids. The solutions derived for the Akbota equation are novel and have not been recorded in previous research. Some of the solutions are shown using 3d, contour, density, and 2d representations created with the Maple software. The accuracy of all solutions has been confirmed.