Abstract
In this article. we implement a new, analytical technique: He's variational iteration Method for solving the coupled KdV and Boussinesq-like equations. In this method, first general Lagrange multipliers are introduced to construct correction functional for the problems. The multipliers in the functional can be identified optimally via the variational theory. Next the components of obtained iteration formulae defined by partial sum of other sequence, specially constructed according to Adomian's decomposition method (ADM). Also according to ADM We Used a partial sum of Adomian polynomials instead of nonlinear terms in iteration formulae. The initial approximations call be freely, chosen with possible Unknown constants, which can be determined by imposing the initial conditions. The results reveal that the proposed method is very effective and can be applied for other nonlinear problems. (C) 2007 Elsevier Ltd. All rights reserved.