Pure gravity traveling quasi‐periodic water waves with constant vorticity

Abstract

AbstractWe prove the existence of small amplitude time quasi‐periodic solutions of the pure gravity water waves equations  with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a Nash‐Moser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic structure. These solutions exist for any fixed value of depth and gravity and restricting the vorticity parameter to a Borel set of asymptotically full Lebesgue measure.