On the solution of two-dimensional coupled Burgers’ equations by variational iteration method A.A. Soliman Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111, Egypt Department of Mathematics, (Bisha Teachers College), King Khalid University, Bisha, P.O. Box. 551, Saudi Arabia Accepted 13 August 2007 Communicated by Prof. Ji-Huan He Abstract By means of variational iteration method the solutions of two-dimensional Burgers’ and inhomogeneous coupled Burgers’ equations are exactly obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is given approximate solu- tions that can converge to its exact solutions faster than those of Adomain’s method. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction Many powerful methods of searching for exact solutions to the nonlinear equations have been proposed. Among these are Backlund transformation [1,5], Darboux transformation [2], Inverse scattering method [3], Hirota’s bilinear method [4], the tanh-function method [6,7], delta-method [8,9], and homotopy perturbation method [10–13]. Recently an extended tanh-function method and symbolic computation are suggested in [14] for solving the new coupled mod- ified KDV equations to obtain four kinds soliton solutions. This method has some merits in contrast with the tanh- function method. It uses a simple algorithm to produce an Algebraic system and also can pick up singular soliton solutions with no extra effort [15–17]. The Burgers’ equation retains the nonlinear aspects of the governing equations in many applications, such as the mathematical model of turbulence [18] and the approximate theory of flow through a shock wave traveling in viscous fluid [19]. Fletcher using the Hopf–Cole transformation [20], gave an analytic solution of the system of two dimensional Burgers’ equations. There are many numerical methods for solving the Burgers’ equa- tion, such as the cubic spline function techniques [21], applied an explicit–implicit method [22], and implicit finite-dif- ference scheme [23]. Soliman [24] used the similarity reductions for the partial differential equations to develop a scheme for solving the Burgers’ equation. Higher-order accurate schemes for solving the two-dimensional Burgers’ equations have been used [25,26]. The coupled system is derived by Esipov [26]. It is a simple model of sedimentation or evolution of scaled volume concentrations of two kinds of particles in fluid suspensions or colloids, under the effect of gravity [27]. 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.08.069 E-mail address: asoliman_99@yahoo.com Chaos, Solitons and Fractals 40 (2009) 1146–1155 www.elsevier.com/locate/chaos