Multiple solutions and dynamical behavior of the periodically excited beta-fractional generalized KdV-ZK system

Abstract In present work, the solutions and dynamics of the beta-fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation is under discussion. By means of traveling wave transformation, the system is transformed into a nonlinear ordinary differential equation. Then some exact traveling wave solutions are obtained by utilizing polynomial complete discrimination system. The rational, trigonometric, hyperbolic and Jacobi elliptic function solutions are obtained, all structures of which are shown in three- or two-dimensions graphs. The dynamics of the system under external periodic perturbation are analyzed from the aspect of phase portraits, bifurcation, Lyapunov exponent, Kaplan-Yorke dimension and sensitivity analysis. These results indicate that the periodically excited system is chaotic. The conclusions of this paper enrich the theory of the fractional generalized KdV-ZK equation and have a guiding role for practical application.