subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. water flow in these systems is described by the boussinesq equation, and the advection-dispersion equation coupled with the boussinesq equation is used to study the solute transport. the objective of this study was to propose a finite difference solution of the advection-dispersi...

Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...

In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...

Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.

the assumptions considered in developing the saint-venant equations limit their application in many practical situations. the modified boussinesq equation was presented to overcome the limitation imposed by saint-venant equation due to the presence of non-hydrostatic pressure distribution and steep slope. in this paper a computational model was developed for solving the modified and the traditi...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

This paper focuses on the 2D incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where Λ= √−Δ denotes the Zygmund operator. Due to the vortex stretching and the lack of sufficient dissipation, the global regularity problem for the supercritical regime α+β<1 remains an outstanding problem. This paper prese...

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is repleni...

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.