Solution of coupled Whitham–Broer–Kaup equations using optimal homotopy asymptotic method

• Whitham–Broer–Kaup (WBK) equation governs the shallow water wave propagation.
• An approximate method namely OHAM is proposed to solve WBK equation.
• The method optimally controls the convergence and adjusts convergence regions.
• OHAM is compared with other methods like VIM and ADM, and also with a numerical method.
• The method is in good agreement with VIM and ADM, but weaker than the numerical one.

In this work, an approximate method called Optimal Homotopy Asymptotic Method (OHAM) is proposed and implemented for the numerical solution of Whitham–Broer–Kaup (WBK) equations with blow-up and periodic solutions. Results obtained through OHAM are compared with the exact as well as with the results available in the literature. It was revealed that only second-order OHAM solutions are sufficient to achieve the desired accuracy in comparison to the higher order solutions of the methods we have made comparison with.