On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy

This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields.