Recently there has been a growing need for the treatment of the nonlinear waterwave problems. In treating the nonlinearity, there are basically two different approaches: One is based on the long-wave approximations or a shallow-water theory that gives an approximate formulation including the effect of the nonlinearity. The other is to treat the Laplace equation defined in the fluid domain with the exact nonlinear free-surface boundary conditions and the exact body-boundary condition if a body

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... present. The former is to treat a simplified nonlinear formulation defined only in a horizontal free-surface plane, which is one dimension less than the original fluid domain. The free-surface flow problems have been of interest to many naval architects and ocean and coastal engineers for a long time. The generation and evolution of the water waves and their interaction with the man-made structures are the main concerns in the problem. The theoretical investigations on the topics have been usually made in the scope of the potential theory by assuming the fluid is inviscid and incompressible. The most distinctive feature of this problem is the