where u (x, t) denotes the unknown function, f (s) is the given nonlinear function, u0 (x) and u1 (x) are the given initial value functions, k is a constant, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and △ denotes the Laplace operator in R. The effects of small nonlinearity and dispersion are taken into consideration in the deriv...

In this paper we consider a three-parameter system of Boussinesq/Boussinesq type, modeling the propagation internal waves. Some theoretical and numerical properties systems were previously analyzed by authors. As second part study, present is concerned with analysis existence simulation some issues dynamics solitary-wave solutions. Standard theories are used to derive several results classical ...

In this paper we review and clarify some aspects of the asymptotic analysis of the compressible Navier Stokes equations in the low Mach number limit. In the absence of heat exchange (the isentropic regime) this limit is well understood and rigorous results are available. When heat exchange is considered different simplified models can be obtained, the most famous being the Boussinesq approximat...

The aim of this paper are in two fold: First, introduce a new simplified bilinear method based on a transformation method combined with the Hirota bilinear sense. Second, apply this new technique to study the time-space fractional Boussinesq equation. To the best of my knowledge, the proposed work present new N-soliton solutions of the fractional Boussinesq equation. These new exact solutions e...

In this paper we examine a spatially two–dimensional forced, damped Boussinesq equation with quadratic nonlinearity. This equation describes small, nonlinear oscillations of a circular, elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for the purpose of constructing solutions for small initial data analytically. The constructive method enables us to perf...

We consider the numerical simulation of a three-dimensional two-phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier-Stokes model and the Boussinesq-Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011] a model problem with a spherical droplet in a Stokes Poiseuille flow with a Bo...

OF THE DISSERTATION Convection in Ethanol-Water Mixtures in the Large Negative Separation Ratio and Non-Boussinesq Regimes

We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d, ηt + ux + ε((ηu)x + auxxx − bηxxt) = 0 ut + ηx + ε(uux + cηxxx − duxxt) = 0. These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott [7], that respective solutions of Boussinesq systems, star...

In the present study, the nonlinear Boussinesq type equation describe the bi-directional propagation of small amplitude long capillary–gravity waves on the surface of shallow water. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional fourth-order nonlinear Boussinesq equation with constant coefficient. These solutions include symm...