Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis

By P. A. Madsen, Harry B. Bingham, H. Schäffer. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003

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A new Boussinesq method for fully nonlinear waves from shallow to deep water (2002, methodology): “Such a procedure is described in Madsen et al. (2002).”
A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry (2006, methodology): “…0.5h, in which case the vertical distribu- tion of the velocity field in fully nonlinear waves is accurate for wave numbers in the interval 0 kh 12 while the dispersion relation and non-linear wave–wave interaction properties are accurate in the interval of 0 kh 25 (see Madsen et al., 2002, 2003).”
A two-layer approach to wave modelling (2004, unknown): “This system for ζ and u1 is identical to the model derived by Nwogu, except for the addition of the ∂h/∂t terms. Additionally, the nonlinear dispersive terms, which have been truncated for the sake of brevity in (3.2) and (3.3), are identical to those derived by Liu (1994) and later implemented nume”
Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation (2009, background): “This is the case because the expansion (29) keeps the nonlocal eects of the Dirichlet-Neumann operator Gµ[",b ] . In [41, 42 , 43], the authors make a dierential approximation of shallow water type based on Pad´e approximants; they show that the dispersive properties remain good far beyond the shal”