A higher order theory for deep water waves

The classical problem of describing the characteristics of deep water waves of finite amplitude is considered. The method of analysis initially follows that of Nekrasov, but differs in that a non-linear algebraic equation is derived. This equation is solved to the third, fifth and fifteenth order by means of a digital computer and the data is presented in tabular form. Expressions for the wave speed and wave shape, predicted by the analysis, are compared with the results obtained by Stokes. The highest wave in water is also discussed