Published online by Cambridge University Press: 24 October 2008
A method employed by the author for a class of boundary-value problems arising in diffraction theory is applied to the problem of the oscillations of water waves on a sloping beach. The two cases of long and short waves are considered. The approach is valid for all values of the parameters and particular cases do not have to be treated separately. It is shown that the present approach enables certain solutions to be obtained which cannot arise in earlier solutions of the problem.