Considered herein are a number of variants of the classical Boussinesq system and their
higher-order generalizations. Such equations were first derived by Boussinesq to describe …

In part I of this work (Bona JL, Chen M and Saut JC 2002 Boussinesq equations and other
systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the …

In this paper, we obtain new nonlinear systems describing the interaction of long water
waves in both two and three dimensions. These systems are symmetric and conservative …

Mathematics | Free Full-Text | A Regularity Criterion in Weak Spaces to Boussinesq
Equations Next Article in Journal Using a Fuzzy Inference System to Obtain Technological …

We construct, analyze and numerically validate a class of conservative, discontinuous
Galerkin schemes for the Generalized Korteweg–de Vries equation. Up to round-off error …

In the present study, we start by formally deriving the simplified phenomenological models of
long-crested shallow-water waves propagating in the equatorial ocean regions with the …

It is suggested here that an interesting and important line of inquiry is the elaboration of
methods of inverse scattering transform (IST) type in contexts where non-homogeneous …

This paper is a continuation of a previous work by two of the authors [J.-C. Saut and Li Xu, J.
Math. Pures Appl.(9), 97 (2012), pp. 635--662.] on long time existence for Boussinesq …

This paper proposes a new, conservative fully discrete scheme for the numerical solution of
the regularized shallow water Boussinesq system of equations in the cases of periodic and …

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations,
are standard fare in the study of small amplitude surface waves in shallow water. While the …