A study of wave trapping between two obstacles in the forced Korteweg-de Vries equation

Abstract

In the forced Korteweg-de Vries equation, a trail of waves can be temporarily trapped between two bumps. Wave propagations vary depending on the solution types and the form of the bumps. In this paper, we study the propagation tendencies of these temporarily trapped waves and especially consider the solitary and flat top solutions over the bumps of different distances and heights. A concept of energy related to wave speeds is defined in the region between the bumps, and it turns out that the trapped waves have to overcome a certain threshold of energy in order to escape out of the region. The numerical investigations are focused on the influence of the distance and the height of the bumps on the energy barrier.