Bifurcation, chaotic behavior, and traveling wave solutions of the space–time fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation

The space–time fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation is a significant nonlinear model used to illustrate numerous physical phenomena, such as water wave mechanics, fluid flow, marine and coastal science, and control systems. In this article, the dynamical behavior of the space–time fractional ZKBBM equation is analyzed, and its traveling wave solutions are investigated based on the theory of the cubic polynomial complete discriminant system. First, the equation is transformed into a nonlinear ordinary differential equation through a complex wave transformation. Then, the dynamical behavior analysis of the equation is using the bifurcation theory from planar dynamical systems. Subsequently, by utilizing the polynomial complete discriminant system and root formulas, several new exact traveling wave solutions of the equation are obtained. Finally, the plots of some solutions are shown using MATLAB software in order to demonstrate their structure.