Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution

In this Letter, two methods for solving nonlinear differential equation known as Variational Iteration and Homotopy Perturbation Methods called respectively VIM and HPM are applied to derive approximate explicit solutions for a special form of generalized nonlinear Benjamin-Bona-Mahony-Burgers equations (BBMB) which may contain high nonlinear terms. Furthermore, the obtained solutions are compared with their corresponding exact solutions to show the applicability, accuracy and finally efficiency of both VIM and HPM in solving a large class of nonlinear physics and engineering problems without the tangible noisy sensitivity to the nonlinear terms or any restrictive assumptions or transformations that may change the physical behavior of the problem.