Propagation of these perturbations is studied from the deep-sea zone to the shallow-water zone through a transition area of variable depth. Two models of the oceanic bottom are considered. In the first model, the bottom is supposed to be flat in the deep-sea and shallow-water areas, and vary in accordance with a linear law in the transition zone. The second model is based on the bottom shape of the region adjacent to the southern Crimean coast. The initial solitary density wave is shown to be transformed into a wave train as time progresses. The velocity field has a patchy structure, being stronger in places where the continental slope is steepest.