非线性KP-BBM方程行波解的动态分析

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

研究了一类受到阻尼扰动和外激励扰动的非线性KP-BBM方程,通过行波变换转化为常微分方程,运用Melnikov方法和数值积分法来计算同宿轨稳定流形和不稳定流形间的距离,得到了该系统在一定参数条件下,孤立波历经倍周期分岔走向混沌之路,并且给出对应的混沌阀值曲线,运用仿真实验验证结论的正确性。

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.