Soliton solutions for the (4+1)-dimensional Fokas equation using integration techniques

In this article, we determine various analytical solutions for the (4+1)-dimensional Fokas equation, a significant model in mathematical physics with numerous applications in nonlinear dynamics. Utilizing multiple integration techniques such as the improved F-expansion technique and the Jacobi elliptic function method, we retrieve an array of solution types, including traveling waves, periodic solutions, bell-shaped waves, rational functions, and both kink and anti-kink structures. We further explore the complex nature of these solutions through their graphical representations. By applying Maple, we visualize our results in three-dimensional (3D), and two-dimensional (2D) formats to illustrate the dynamic behavior of these solutions across various parameters and initial conditions. Our findings provide deeper insights into the properties of the Fokas equation and offer a valuable reference for further studies in nonlinear wave phenomena. © 2024 Faculty of Engineering, Alexandria University