Edge capillary-gravity waves on a sloping beach

It is shown how the solution for velocity potential may be determined when the effect of surface tension is included in the linearized theory of Ursell-type edge waves over a plane-sloping beach. The problem is examined without making a hydrostatic assumption. Explicit solutions for edge capillary-gravity waves are given and the dispersion equation is obtained. The influence of capillarity on gravity waves is discussed.