We review here the derivation of many of the most important models that appear in the
literature (mainly in coastal oceanography) for the description of waves in shallow water. We …

This study deals with higher-order asymptotic equations for the water-waves problem. We
considered the higher-order/extended Boussinesq equations over a flat bottom topography …

In this work we prove that the solution of the Serre-Green-Naghdi equation cannot be
globally defined when the interface reaches the impervious bottom tangentially. As a …

We study the qualitative behavior of the Boussinesq–Burgers equations on a finite interval
subject to the Dirichlet type dynamic boundary conditions. Assuming H 1× H 2 initial data …

We establish the long time existence of solutions for the “Boussinesq-Full dispersion”
systems modeling the propagation of internal waves in a two-layer system. For the two …

This paper is concerned with the one-dimensional version of a specific member of the (abcd)
family of Boussinesq systems having the higher possible dispersion and eigenvalues with …

We prove a long time existence result for the solutions of a two-dimensional Boussinesq
system modeling the propagation of long, weakly nonlinear water waves. This system is …

We prove the existence on long time scales of the solutions to the Cauchy problem for a
version of weakly transverse Boussinesq systems arising in the modeling of surface water …

This essay is concerned with long-crested waves such as those arising in bore propagation.
Such motions obtain on rivers when a surge of water invades an otherwise constantly …

In this article, we propose finite volume schemes for the $ abcd $-systems and we establish
stability and error estimates. The order of accuracy depends on the so-called BBM-type …