It is well known that the Boussinesq equation is the bidirectional equivalent of the celebrated Korteweg-de Vries equation. Here we consider Boussinesq-type versions of two classical unidirectional integrable equations. A procedure is presented for deriving multisoliton solutions of one of these equations – a bidirectional Kaup–Kupershmidt equation. These solitons have the unusual property that...

This paper modeled heating air of a room through examining free convection in a 3D chamber. The chamber had cold and hot sources with Tc and Th temperatures, respectively. Its other walls were adiabatic. This study aimed at predicting effect of temperature difference, displacement of hot and cold sources and their aspect ratio on flow field, temperature and heat transfer rate. To conduct the st...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

We study the global well-posedness of the Lagrangian averaged Euler equations in three dimensions. We show that a necessary and sufficient condition for the global existence is that the BMO norm of the stream function is integrable in time. We also derive a sufficient condition in terms of the total variation of certain level set functions, which guarantees the global existence. Furthermore, we...

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

Using the algebraic method of Gardner’s deformations for completely integrable systems, we construct recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup–Boussinesq equations. By extending the Magri schemes for these equations, we obtain new integrable systems adjoint with respect to the initial ones and describe their Hamiltonian structures and symmetry proper...

A numerical study of the natural convection of the laminar heat transfers in the stationary state was developed in a horizontal ring and compared between a heated trapezoidal internal cylinder and a cold elliptical outer cylinder. This annular space is traversed by a Newtonian and incompressible fluid. The Prandtl number is set to 0.7 (air case) for different Rayleigh numbers. The system of equ...

We study in this paper the correlation between buoyancy flux, efficiency of energy dissipation and linear nonlinear components potential vorticity, PV, a point-wise invariant Boussinesq equations, contrasting three identified regimes rotating stratified turbulence, namely wave-dominated, wave–eddy interactions eddy-dominated. After recalling some main novel features these flows compared to homo...