Numerical simulation of solitary waves on plane slopes

In this paper, we present a numerical method for the computation of surface water waves over bottom topography. It is based on a series expansion representation of the Dirichlet–Neumann operator in terms of the surface and bottom variations. This method is computationally very efficient using the fast Fourier transform. As an application, we perform computations of solitary waves propagating over plane slopes and compare the results with those obtained from a boundary element method. A good agreement is found between the two methods.