Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework

Abstract

In this work we asymptotically and numerically studied the interaction of large amplitude solitary waves with an external periodic force using the forced extended Korteweg-de Vries equation (feKdV). Regarding these interactions, we found three types of regimes depending on the amplitude of the solitary wave and how its speed and the speed of the external force are related. A solitary wave can remain steady when its crest and the crest of the external force are in phase, it can bounce back and forth remaining close to its initial position when its speed and the external force speed are near resonant, or it can move away from its initial position without reversing its direction. Additionally, we verified that the numerical results agreed qualitatively well within the asymptotic approximation theory for external broad forces.