Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
Language: English
Published by American Mathematical Society, US, 2024
- Softcover
- New
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Condition: New
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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.…
Seller Inventory # LU-9781470468774
- Title
- Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
- Author
- Roberto Feola, Filippo Giuliani
- Publisher
- American Mathematical Society, US
- Publication year
- 2024
- Condition
- New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1470468778
- ISBN 13
- 9781470468774
- Item weight
- 272 grams
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.
"Synopsis" may belong to another edition of this title.
About the Author
Filippo Giuliani, Politecnico di Milano, Italy.
"About the title" may belong to another edition of this title.
Rarewaves.com UK
London, United Kingdom
AbeBooks seller since June 11, 2025
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