We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated. Keywords—Shock, Soliton, Coupling, Superthermal ions.

In this paper, we construct an analytical solution of the coupled Burgers’ equation, using homotopy analysis method, which is a semi-analytical approximate obtained by method convergent for different values convergence control parameter ℏ, optimal value ℏ corresponding with minimum error to be determined residual. The results present are compared other solutions numerical methods.

In this paper, we shall use the variational iteration method to introduce a framework for analytic treatment of linearized Burgers’ equation and coupled Burgers’ equations in 2dimensional space. For these equations, the exact solutions are obtained. The paper confirms the power and efficiency of the method in reducing the size of the calculation, also the simplicity of the method compared with ...

Purpose – The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers’-type nonlinear partial differential equations. Design/methodology/approach – The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by Ru...

This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The velocity of sedimentation (or creaming) depends upon the volume fraction of the constituting particles and leads to Burgers-like equations for concentration profil...

We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a secondorder approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages ...

In this paper, the reduced differential transform method (RDTM) is applied to various nonlinear evolution equations, Korteweg–de Vries Burgers' (KdVB) equation, Drinefel’d–Sokolov–Wilson equations, coupled Burgers equations and modified Boussinesq equation. Approximate solutions obtained by the RDTM are compared with the exact solutions. The present results are in good agreement with the exact ...

A 2 1 dimensional Burgers equation and a coupled higher dimensional Burgers system is studied by the singular manifold method. The Bäcklund transformations are obtained. Some interesting exact solutions are given. Then localized structures, such as dromion and solitoff, are found, and their interaction properties are numerically studied. The fusion phenomena of two dromions, a dromion and a sol...