Shallow water waves over an uneven bottom and an inhomogeneous KP equation

Three-dimensional shallow water waves over an uneven bottom are considered. The depth is assumed to be slow in variation. As a model, an inhomogeneous Kadomtsev-Petviashvili equation is presented. Some reductions of this equation are used to describe deformation of a line soliton due to the depth change. The model equation is valid for a wide class of two-dimensional nonlinear waves in inhomogeneous systems.