We present the recent result [9] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash–Moser scheme, Birkho¤ normal form methods and pseudo-di¤erential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations.

Feola, R., & Giuliani, F. (2020). Time quasi-periodic traveling gravity water waves in infinite depth. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 31(4), 901-916 [10.4171/RLM/919].

Time quasi-periodic traveling gravity water waves in infinite depth

Feola R.;Giuliani F.
2020

Abstract

We present the recent result [9] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash–Moser scheme, Birkho¤ normal form methods and pseudo-di¤erential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations.
Feola, R., & Giuliani, F. (2020). Time quasi-periodic traveling gravity water waves in infinite depth. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 31(4), 901-916 [10.4171/RLM/919].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/397001
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