The conduit equation is a dispersive non-integrable scalar equation modeling the flow of a
low-viscous buoyant fluid embedded in a highly viscous fluid matrix. This equation can be …

This paper is devoted to the theoretical and numerical investigation of the initial boundary
value problem for a system of equations used for the description of waves in coastal areas …

We present a framework for constructing a first-order hyperbolic system whose solution
approximates that of a desired higher-order evolution equation. Constructions of this kind …

Résumé The primary focus of this work is the coupling of dispersive free-surface flow models
through the utilization of a thick interface coupling technique. The initial step involves …

A complete study of the modulation equations for the Benjamin–Bona–Mahony equation is
performed. In particular, the boundary between the hyperbolic and elliptic regions of the …

We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries
equation (KdV). We show that this approximation, which we call KdVH, possesses a rich …

The primary focus of this work is the coupling of dispersive free-surface flow models through
the utilization of a thick interface coupling technique. The initial step involves introducing a …

This habilitation manuscript gathers the work I have done in recent years. They mainly focus
on the study of the stability and the multiscale analysis of finite difference methods for the …

This work deals with wave propagation into a coaxial cable, which can be modelled by the
3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's …

The goal of this special issue is to provide an overview of recent progress in the area of
numerical methods and applications for ocean waves in the coastal environment, to identify …