A new approach to high-order Boussinesq models

An infinite-order, Boussinesq-type differential equation for wave shoaling over variable bathymetry is derived. Defining three scaling parameters-nonl inearity, the dispersion parameter, and the bottom slope-the system is trun cated to a finite order. Using Pade approximants the order in the dispersio n parameter is effectively doubled. A derivation is made systematic by sepa rately solving the Laplace equation in the undisturbed fluid domain and the n addressing the nonlinear free-surface conditions. We show that the nonlin ear interactions are faithfully captured. The shoaling and dispersion compo nents are time independent.