Quasi-periodic traveling waves on an infinitely deep fluid under gravity

  title={Quasi-periodic traveling waves on an infinitely deep fluid under gravity},
  author={Roberto Feola and Filippo Giuliani},
  journal={arXiv: Analysis of PDEs},
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the first existence result of quasi-periodic water waves solutions bifurcating from a \emph{completely resonant} elliptic fixed point. The proof is based on a Nash-Moser scheme, Birkhoff normal form methods and pseudo-differential calculus techniques. We deal with… 
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