Asymptotic Behavior of a Shallow-Water Soliton Reflected at a Sloping Beach
This paper deals with a long-time asymptotic behavior of a shallow water soliton reflected at a sloping beach. Based on the edge-layer theory, it is shown that the boundary-value problem for the Boussinesq equation under the “reduced” boundary condition is simplified to an “initial value” problem for the Korteweg-de Vries equation in the form of the spatial evolution of the reflected wave. Solving it numerically, the asymptotic behavior is demonstrated and compared with the one which evolves from the “initial value” obtained by solving the full nearshore behavior by the boundary element method.
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