Context. Three-dimensional spherical dynamo simulations carried out within the framework of the anelastic approximation have revealed that the established distinction between dipolar and multipolar dynamos tends to be less clear than it was in Boussinesq studies. This result was first interpreted as a direct consequence of the existence of a larger number of models with a high equatorial dipole...

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 the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and...

In this Letter, we study Kaup-Boussinesq system by using the wellknown He’s variational approach. In fact, the He’s variational method is a promising method to various systems of linear and nonlinear equations.

We consider a modified Boussinesq type equation. The Painlevé test of the WTC method is performed for this equation and it shows that the equation has weak Painlevé property. Some exact solutions are constructed.

We propose a novel approach for bridging the Boussinesq equations and the primitive equations. This approach uses spatio-temporal filtering as an alternative to traditional scaling arguments. © 2009 Elsevier Ltd. All rights reserved.

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

We show that we can also apply the Hirota method to some nonintegrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these equations.

Considered herein are certain Boussinesq systems with the presence of large surface tension. The existence and stability of solitary waves are established by using techniques introduced earlier by Buffoni [7] and Lions [9, 10].