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Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity.
・ISBN 978-1-4704-6877-4 paper US$ 85.00
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| 著者・編者 | Feola, Roberto / Giuliani, Filippo, |
|---|---|
| シリーズ | (Memoirs of the American Mathematical Society) |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2024 |
| ページ数 | 164 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A03-4595＞ |
解説
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.
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.