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Overview"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 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 the combined problems of small divisors and the fully-nonlinear nature of the equations. The lack of parameters, like the capillarity or the depth of the ocean, demands a refined nonlinear bifurcation analysis involving several nontrivial resonant wave interactions, as the well-known ""Benjamin-Feir resonances"". We develop a novel normal form approach to deal with that. Moreover, by making full use of the Hamiltonian structure, we are able to provide the existence of a wide class of solutions which are free from restrictions of parity in the time and space variables." Full Product DetailsAuthor: Roberto Feola , Filippo GiulianiPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: Volume: 295 Number: 1471 ISBN: 9781470468774ISBN 10: 1470468778 Pages: 164 Publication Date: 31 May 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Forthcoming Availability: Not yet available This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Table of ContentsReviewsAuthor InformationRoberto Feola, Universita degli Studi Romatre, Rome, Italy. Filippo Giuliani, Politecnico di Milano, Italy. Tab Content 6Author Website:Countries AvailableAll regions |