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Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
By (author) Roberto Feola, By (author) Filippo Giuliani
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| book description |
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.
| product details |
Normally shipped |
Publisher | American Mathematical Society
Published date | 31 May 2024
Language |
Format | Paperback / softback
Pages | 164
Dimensions | 254 x 178 x 0mm (L x W x H)
Weight | 272g
ISBN | 978-1-4704-6877-4
Readership Age |
BISAC | science / mathematical physics
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