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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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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 Nashâ€“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.

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Bonsai Success in Southern Africa

Carl Morrow
Paperback / softback
160 pages
was: R 320.95
now: R 288.95
Stock is usually dispatched in 6-12 days from date of order

In this uniquely Southern African book, Carl Morrow and Keith Kirsten guide readers step by step into the magical realms of bonsai as a hobby, horticultural practice and art form.

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The Ballerina and the Bull: Anarchist Utopias in the Age of Finance

Johanna Isaacson
Paperback / softback
288 pages
was: R 306.95
now: R 275.95
This title will take longer to obtain, and should be delivered in 6-8 weeks

Our moment has seen the resurgence of an anarchist sensibility, from the uprisings in Seattle in 1999 to the Occupy movement of 2011.

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Fifteen Dogs

AndrÃ© Alexis
Paperback / softback
176 pages
was: R 280.95
now: R 252.95
Available from overseas. Dispatched in aprox 4-8 weeks as local supplier is out of stock

A pack of dogs are granted the power of human thought - but what will it do to them? A surprising and insightful look at the beauty and perils of consciousness.

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