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• W2000817986 abstract "This paper presents a Hamiltonian formulation of the water-wave problem in which the non-local Dirichlet-Neumann operator appears explicitly in the Hamiltonian. The principal long-wave approximations for water waves are derived by the systematic approximation of the Dirichlet-Neumann operator by a sequence of differential operators obtained from a convergent Taylor expansion of the Dirichlet-Neumann operator. A simple and satisfactory method of obtaining the classical two-dimensional approximations such as the shallow-water, Boussinesq and KdV equations emerges from the process. A straightforward transformation theory describes the relationship between the classical symplectic structure appearing in the water-wave problem and the various non-classical symplectic structures that arise in long-wave approximations. The discussion extends to include three-dimensional approximations, including the KP equation." @default.
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• W2000817986 date "1994-06-01" @default.
• W2000817986 modified "2023-09-29" @default.
• W2000817986 title "Hamiltonian long-wave approximations to the water-wave problem" @default.
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• W2000817986 doi "https://doi.org/10.1016/0165-2125(94)90003-5" @default.
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