Approximate traveling wave solutions for coupled Whitham–Broer–Kaup shallow water

Homotopy Perturbation Method (HPM) was used for computing the Coupled Whitham–Broer–Kaup Shallow Water. Then HPM solution verified against exact one and compared with another approximate solution, the Homotopy Analysis Method (HAM). The existent error of the methods computed and convergence of the HPM solution has presented. Results reveal that HPM is an effective and powerful in solving the non-linear systems in mechanic, analytically.