Author(s)

M. Rahman

Abstract

In the study of water waves, it is well known that linear theory provides a first approximation to the complete wave motion. In order to approach the complete solution more closely, successive approximations using per- turbation procedure are usually developed. In his classic paper in 1847, Stokes first established the nonlinear solution for periodic plane waves on deep water. The convergence towards a complete solution does not occur for steeper waves, unless a different perturbation parameter from that of Stokes is chosen. This paper discusses the wave motion when the wave am- plitude is large compared to the wavelength. It has been confirmed that the analytical results are valid only for deep water waves. Then the investiga- tion is carried out to obtain the solution of the shallow water wave theory using perturbation metho

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