Trapped solitary waves and collisions for the forced Korteweg-de Vries equation

TL;DR

This paper investigates trapped solitary waves and their collisions in the forced Korteweg-de Vries equation, revealing how waves bounce between obstacles, escape, and interact under various conditions through numerical simulations.

Contribution

It provides new insights into the behavior of trapped waves and their collisions in a forced KdV system, including escape dynamics and interaction effects.

Findings

Waves remain trapped bouncing between obstacles until a momentum threshold is exceeded.

The escape time of trapped waves varies linearly with obstacle distance.

Wave collisions are affected by interactions but show limited statistical impact.

Abstract

The aim of this work is to study trapped waves and their collisions between two topographic obstacles for the forced Korteweg-de Vries equation. Numerical simulations show that solitary waves remain trapped bouncing back and forth between the obstacles until the momentum overcomes a certain threshold. We find that the waves have a certain tendency of escaping out upstream. Furthermore, the time of escape of the trapped wave varies linearly with the distance between the bumps. Besides, we study collisions of solitary waves between the obstacles. Although the dynamic of one wave is affected by the other one, statistically this feature is not evident.