Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Publication Details

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences vol. 376, no. 2111 (August 2017).

Abstract

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth.

DOI

10.1098/rsta.2017.0091

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