The generation of symmetric and asymmetric lumps by a bottom topography

A lump solution to the (2+1)-dimensional Kadomtsev-Petviashvili I (KPI) equation is presented by making use of Hirota bilinear transform method. Moreover, the generation of symmetric and asymmetric lumps by a straight and oblique three-dimensional bottom topography is numerically investigated using the forced Kadomtsev-Petviashvili I (fKPI) equation. The wave structures and propagation properties are studied for several forcings, such as the orientation and volume of the different bottom topographies. The main result is the asymmetric generation of skew lumps downstream of the obstacle for obliquely placed topographies. Another finding is the generation of two pairs of lumps by a stronger forcing. The second pair of lumps with a smaller amplitude and propagation speed, but with a larger propagation angle with respect to the x-axis than those of the first pair of lumps is generated with a larger period. The final finding is that the amplitude and velocity of the lumps depend strongly on the parameters of different topographies, and the propagation angles of lumps are insensitive to the parameters of different topographies.