Approximate soliton solutions for a (2+1)(2+1)-dimensional Broer–Kaup system by He’s methods

In this paper, two methods for solving a nonlinear differential equation known as He’s variational iteration and homotopy perturbation methods are applied to derive the approximate kink-type soliton solutions for a new (2+1)-dimensional simplified generalized Broer–Kaup system. Furthermore, the solutions obtained are compared with the corresponding exact solution to show the applicability, accuracy and, finally, efficiency of the present methods in solving a large class of nonlinear physics and engineering problems without substantial noisy sensitivity to the nonlinear terms or any restrictive assumptions or transformations that may change the physical behavior of the problems.