The wave stability of solitary waves over a bump for the full Euler equations

In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow and the other from the perturbed solitary-wave flow. We find that steady waves from the perturbed uniform flow are always stable with respect to perturbations of its amplitude. Regarding the perturbed solitary wave, when the perturbed initial condition has smaller amplitude than the steady solution, we notice a certain type of stability. Yet, when the perturbed initial condition has larger amplitude than the steady solution an onset of wave-breaking seem to occur.