Traveling Wave Solutions of WBK Shallow Water Equations by Differential Transform Method

By using differential transform method (DTM) to coupled Whitham–Broer–Kaup (WBK), we find the explicit traveling wave solutions of WBK equations in the form of a convergent polynomial series. In addition two examples the special case of WBK equations namely modified Boussinesq (MB) and approximate long wave (ALW) equations are discussed in details and compared with previous solutions. The obtained results demonstrate the reliability of the algorithm and the DTM is an attractive method in solving the systems of nonlinear differential equations.

Differential transform method (DTM), Whitham–Broer–Kaup equations, Approximate long wave equation, Boussinesq equation