  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 waves over arbitrary
bathymetry, Papoutsellis and Athanassoulis (2017) (arXiv:1704.03276).
Applications considered herein concern the interaction of solitary waves with
bottom topographies and vertical walls both in two- and three-dimensional
environments. The essential novelty is a new representation of the
Dirichlet-to-Neumann operator, needed to close the Hamiltonian evolution
equations. This representation emerges from the treatment of the substrate
kinematical problem by means of exact semi-separation of variables in the
irregular fluid domain, established recently by Athanassoulis & Papoutsellis
(2017) (https://doi.org/10.1098/rspa.2017.0017). The HCMT ensures an efficient
dimensional reduction of the exact NLFP, being able to treat an arbitrary
bathymetry as simply as the flat-bottom case. A key point for the efficient
implementation of HCMT is the fast and accurate evaluation of the space-time
varying coefficients appearing in some of its equations. All varying
coefficients are calculated analytically, resulting in a refined version of the
theory, characterized by improved accuracy at significantly reduced
computational time. This improved version of HCMT is first validated against
existing experimental results and other computations, and subsequently applied
to new solitary wave-bottom interaction problems. The latter include: i) the
investigation of a new type of Bragg scattering effect, appearing when a
solitary wave propagates over a seabed with a sinusoidal patch, and ii) the
disintegration, focusing and reflection of a solitary wave moving over a
three-dimensional bathymetry consisting of parallel banks and troughs, and
impinging on a vertical wall.
