Related papers: Fully dispersive Boussinesq models with uneven bat…
We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled…
In this paper, we investigate the time of existence of the solutions to two full dispersion models derived from the water waves equations in the shallow water regime: the Whitham equation and a Whitham-Boussinesq system in dimension one and…
The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…
In this paper we are concerned with a nonlocal system to model the propagation of internal waves in a two-layer interface problem with rigid lid assumption and under a Boussinesq regime for both fluids. The main goal is to investigate…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and…
In this work, we numerically study the higher-ordered/extended Boussinesq system describing the propagation of water-waves over flat topography. A reformulation of the same order of precision that avoids the calculation of high order…
By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can…
We study the stability of special, stratified solutions of a 3d Boussinesq system describing an incompressible, inviscid 3d fluid with variable density (or temperature, depending on the context) under the effect of a uni-directional…
This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…
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-dimensional Hamiltonian case we prove the global existence of small…
We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model"…
Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by…
In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the…
We consider here different family of Boussinesq systems in two space dimensions. These systems approximate the three-dimensional Euler equations and consist of three coupled nonlinear dispersive wave equations that describe propagation of…
A coupled BBM system of equations is studied in the situation of water waves propagating over decreasing fluid depth. A conservation equation for mass and a wave breaking criterion valid in the Boussinesq approximation is found. A Fourier…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are…
We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative…