Free surface flows occur frequently in our daily lives and many natural or industrial settings.
Our understanding of such flows has grown tremendously with progress in mathematical …

There exists a growing literature on using the Fokas method (unified transform method) to
solve Laplace and Helmholtz problems on convex polygonal domains. We show here that …

We compare the effectiveness of solving Dirichlet–Neumann problems via the Craig–Sulem
(CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM …

Bathymetry is an important factor affecting wave propagation in coastal environments but is
often challenging to measure in practice. We propose a method for inferring coastal …

The inverse problem of steady two-dimensional open channel free-surface flow is
considered, with the focus on determining two types of disturbances: a surface pressure …

Recent work has given rise to a novel and simple numerical technique for solving elliptic
boundary value problems formulated in convex polygons in two dimensions. The method …

We analyze an inverse problem for water waves posed by Richard Feynman in the BBC
documentary Fun to Imagine. We show that the problem can be modeled as an inverse …

The main focus of this paper is to derive a direct relationship between the surface of an
inviscid traveling gravity wave in two dimensions, and the pressure at the bottom of the fluid …

In this paper, we consider a problem inspired by the real‐world need to identify the
topographical features of ocean basins. Specifically, we consider the problem of estimating …

The direct problem of water-wave equations is the problem of determining the surface and
its velocity potential, in time T>0, for a given initial profile and velocity potential, where the …