Dynamics investigation of the (4+1)-dimensional Fokas equation using two effective techniques

The (4+1)-dimensional Fokas equation is investigated in this paper. The solutions of (4+1)-dimensional Fokas equation are obtained via two methods, naming modified auxiliary equation method and modified extended direct algebraic method. The proposed methods are efficient and stable. Many novel solutions of (4+1)-dimensional Fokas equation are obtained. The obtained solutions include the trigonometric functions, hyperbolic functions, rational functions and Jacobi elliptic functions. The dynamical behavior of retrieved solutions is illustrated by simulation of graphs. The 3D-surface graphs, 2D contour graphs, 2D-line graphs and density graphs of obtained solutions are plotted by utilizing the softwares like Maple and Mathematica. It is hoped that the acquired solutions will help to comprehend the variety of physical phenomena and dynamical processes. •The (4 + 1)-dimensional Fokas equation is investigated in this paper.•The solutions of (4+1)-dimensional Fokas equation are obtained via two exact methods.•The proposed methods are efficient and stable.•Trigonometric, hyperbolic, rational and Jacobi elliptic functions solutions are found.•The dynamical behavior of retrieved solutions is illustrated by graphs.