The influence of variable surface tension on capillary-gravity waves

Periodic gravity-capillary waves propagating at a constant velocity at the surface of a fluid of infinite depth are considered. The surface tension is assumed to vary along the free surface. A numerical procedure is presented to solve the problem with an arbitrary distribution of surface tension on the free surface. It is found that there are many different families of solutions. These solutions generalize the classical theory of gravity-capillary waves with constant surface tension. An asymptotic solution is presented for a particular distribution of variable surface tension.