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

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.