A novel approach for the description of both wave propagation and flow circulation in the
nearshore zone has been defined. This is based on an integro-differential system which, at …

We study numerically the propagation of solitary waves in a Hamiltonian nonlocal shallow
water model for bidirectional wave propagation in channels of variable depth. The derivation …

We consider the two‐dimensional water wave problem in an infinitely long canal of finite
depth both with and without surface tension. It has been proven by several authors that long …

The present study is devoted to the problem of tsunami wave generation. The main goal of
this work is twofold. First of all, we propose a simple and computationally inexpensive model …

We study here some asymptotic models for the propagation of internal and surface waves in
a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves …

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a
stratified fluid, and experiences an important drag due to waves below the surface. More …

We are interested in asymptotic models for the propagation of internal waves at the interface
between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review …

We are interested in the Korteweg–de Vries (KdV), Burgers and Whitham limits for a spatially
periodic Boussinesq model with non-small contrast. We prove estimates of the relations …

We present new models to describe shallow water flows over non smooth topographies. The
water waves problem is formulated as a system of two equations on surface quantities in …

This article provides a survey on some main results and recent developments in the
mathematical theory of water waves. More precisely, we briefly discuss the mathematical …