Exploring bifurcation, phase portraits, and exact solutions of the Fokas equation using the improved Cham method

In this paper, we provide a thorough investigation of the bifurcations of the Fokas equation and a detailed analysis of its associated phase portraits. We examine the bifurcation phenomena, identify bifurcation points, and analyze their behavior through graphical representations. In addition, we propose the improved Cham method to derive exact solutions, which enables us to explore a wide range of cases and gain a better understanding of the associated phenomena. We also conduct a singularity analysis to determine the conditions under which these exact solutions remain nonsingular and bounded. The findings of this study make a significant contribution to the understanding of the Fokas equation and its dynamics, offering novel solutions and visualizing their corresponding phase portraits.