KdV & KAM (Hardcover, 2003 ed.)

In this text the authors consider the Korteweg-de Vries (KdV) equation (ut = - uxxx + 6uux) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are periodic, quasi-periodic or almost-periodic in time. Also, their construction leads to some new results along the way. Subsequently, these coordinates allow us to apply a general KAM theorem for a class of integrable Hamiltonian pde's, proving that large families of periodic and quasi-periodic solutions persist under sufficiently small Hamiltonian perturbations. The pertinent nondegeneracy conditions are verified by calculating the first few Birkhoff normal form terms -- an essentially elementary calculation.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 45
Release date:	May 2003
First published:	2003
Authors:	Thomas Kappeler • Jurgen Poeschel
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Hardcover
Pages:	279
Edition:	2003 ed.
ISBN-13:	978-3-540-02234-3
Categories:	Books > Science & Mathematics > Mathematics > General Books > Children's & Educational > Mathematics > General Books > Children's Fiction & Fun Books > Academic & Education > Primary & Secondary Education Promotions
LSN:	3-540-02234-1
Barcode:	9783540022343

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