Dynamic analysis for travelling wave solutions of the nonlinear KP-BBM equation

The nonlinear KP-BBM system with damping perturbation and external excitation disturbance is studied. By using a traveling wave transform, an ordinary differential equation is established. A Melnikov method and a numerical integral method are presented to compute the distance of a stable manifold and an unstable manifold for a homoclinic orbit, and under some parameter conditions a plot of thresholds above which chaos may occur is obtained, which implied that solitary waves undergo period doubling bifurcation and become eventually chaos. Finally simulations are carried out for this system.