Solitary wave interactions with a periodic forcing: the extended Korteweg-de Vries framework

TL;DR

This paper numerically investigates how large amplitude solitary waves interact with external periodic forcing within the extended Korteweg-de Vries framework, revealing resonant bouncing and non-reversing behaviors.

Contribution

It introduces a numerical study of solitary wave interactions with periodic forcing using the extended KdV equation, highlighting resonant and non-resonant dynamics.

Findings

Solitary waves can bounce near their initial position under resonant forcing.

Waves can move away without reversing direction.

Numerical results align well with asymptotic approximations for broad forcings.

Abstract

The aim of this work is to study numerically the interaction of large amplitude solitary waves with an external periodic forcing using the forced extended Korteweg-de Vries equation (feKdV). Regarding these interactions, we find that a solitary wave can bounce back and forth remaining close to its initial position when the forcing and the solitary wave are near resonant or it can move away from its initial position without reversing their direction. Additionally, we verify that the numerical results agree well within the asymptotic approximation for broad the forcings.