This paper deals with the implementation of a new, efficient, non-perturbative, Hamiltonian
coupled-mode theory (HCMT) for the fully nonlinear, potential flow (NLPF) model of water …

A novel coupled-mode model is developed for the wave–current–seabed interaction
problem, with application in wave scattering by non-homogeneous, sheared currents over …

This document is an announcement and preview of a memoir whose full version is available
on the Open Math Notes repository of the American Mathematical Society (OMN …

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-
surface potential flow are presented, tested, and validated. The first is an extension of …

The modeling of wave-breaking dissipation in coastal areas is investigated with a fully
nonlinear and dispersive wave model. The wave propagation model is based on potential …

The Alber equation is a phase-averaged second-moment model used to study the statistics
of a sea state, which has recently been attracting renewed attention. We extend it in two …

For a waveguide that is invariant in one of the horizontal directions, this paper presents a
mathematically exact partial-wave decomposition of the wavefield for assessment of multiple …

This paper considers the analytic methods for finding solutions of the Korteweg-Devries
(KdV) equation, a nonlinear evolution-type partial differential equation (PDE), that describes …

A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable
bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in …

Coupled-mode methods have been used in underwater acoustics to compute three-
dimensional sound propagation and scattering. Significant computational simplifications are …