  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.
