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＜電子ブック＞
KdV & KAM / by Thomas Kappeler, Jürgen Pöschel
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 45)

版	1st ed. 2003.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2003
本文言語	英語
大きさ	XIII, 279 p : online resource
冊子体	KdV & KAM / Thomas Kappeler, Jürgen Pöschel
著者標目	*Kappeler, Thomas author Pöschel, Jürgen author SpringerLink (Online service)
件　名	LCSH:Education LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematics LCSH:Dynamical systems LCSH:Differential equations LCSH:Mathematical physics FREE:Education FREE:Global Analysis and Analysis on Manifolds FREE:Mathematics FREE:Dynamical Systems FREE:Differential Equations FREE:Mathematical Methods in Physics
一般注記	I The Beginning -- II Classical Background -- III Birkhoff Coordinates -- IV Perturbed KdV Equations -- V The KAM Proof -- VI Kuksin’s Lemma -- VII Background Material -- VIII Psi-Functions and Frequencies -- IX Birkhoff Normal Forms -- X Some Technicalities -- References -- Notations 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-08054-2

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