Abstract
The homotopy perturbation method (HPM) is employed to find the explicit and numerical traveling wave solutions of Whitham–Broer–Kaup (WBK) equations, which contain blow-up solutions and periodic solutions. The numerical solutions are calculated in the form of convergence power series with easily computable components. The homotopy perturbation method performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.
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