Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity / Roberto Feola, Filippo Giuliani.

Format:

Book

Author/Creator:

Feola, Roberto, author.

Giuliani, Filippo, author.

Series:

Memoirs of the American Mathematical Society ; no. 1471.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1471

Language:

English

Subjects (All):

Nonlinear waves.

Physical Description:

v, 158 pages ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2024]

Summary:

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.

Notes:

Includes bibliographical references (pages 155-158).

ISBN:

9781470468774

1470468778

OCLC:

1429659489