The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each ...

(Received July 23, 2013; in nal form February 26, 2014) In this paper, the (G′/G, 1/G) and (1/G′)-expansion methods with the aid of Maple are used to obtain new exact traveling wave solutions of the Boussinesq equation and the system of variant Boussinesq equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. ...

We study the Boussinesq equation from the point of view of a multipletime reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg–de Vries hierarchy, we show that the solitary–wave of the Boussinesq equation is a solitary–wave satisfying simultaneously all equations of the Korteweg–de Vries hierarchy, each one in an appro...

The characteristics of photovoltaic (PV) panels in the field conditions are to be obtained using a fast varying load. The paper presents a simple electronic load for testing a set of PV panels using linear metal oxide field effect transistors (MOSFETs). The proposed test set up gives the current versus voltage and power versus voltage characteristics of PV panels by quickly scanning the load. D...

This paper establishes the global existence and uniqueness of solutions to a generalized 2D Euler-Boussinesq systems of equations with a logarithmically supercritical velocity.

In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. So, we use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow (and not deep) water. In order to justify our derivation, we check it by deriving the viscous Korteweg-...