Generation of trapped depression solitary waves in gravity-capillary flows over an obstacle

In this work, we investigate trapped gravity-capillary waves resonantly excited by an accelerated submerged obstacle in a shallow water channel. The problem is studied in the fifth-order forced Korteweg-de Vries equation framework. The solution of the initial value problem for this equation is computed numerically through a pseudospectral method with integrating factor. When the water surface is initially taken at rest, we identify regimes in which depression solitary waves are generated and later trapped in a vicinity of the obstacle. The wave stability of these trapped waves is studied numerically by disturbing their amplitudes as well as the amplitude of the submerged obstacle. Besides, when considering the topographic obstacle as a hole, we identify regimes in which multiple depression solitary waves are generated and then trapped.