Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves

Source abstract

We prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x x ) of a 2 2 -dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.