Research in recent years shows that a number of physically significant problems can be modelled by coupled nonlinear wave equations. It is observed that most of such equations exhibit solitary wave solutions which reveal the important properties of the system concerned. In this work, we consider a coupled system which describes the propagation of dispersive water waves. By an explicit analytical method we demonstrate several solutions of the equation. It is worth remarking that under certain conditions solitary wave solutions can be obtained. Finally, some interesting results are also found by introducing cubic nonlinearity in the basic system. © 1990 IOP Publishing Ltd.