Abstract
This article reviews reflection and transmission of a shallow water soliton incident upon a boundary or an obstruction such as a sloping beach, a stepped bottom or a submerged barrier. Introducing a concept of edge-layer, the matched asymptotic expansion method is applied to obtain uniformly valid solutions throughout the whole region. The matching condition yields a 'reduced' boundary condition to be imposed on the Boussinesq equation in the shallow-water region extending on the outside of the edge-layer. Explicit matching procedure is demonstrated in detail for the sloping beach and is briefly described for the step and the barrier. Solving the Boussinesq equation (s) under the 'reduced' boundary condition (s) thus derived, reflection (and transmission) is discussed for the three typical bottom topography.
