KdV & KAM / by Thomas Kappeler, Jürgen Pöschel
(Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics ; 45)
| データ種別 | 電子ブック |
|---|---|
| 版 | 3. Folge |
| 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 |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Kappeler, Thomas author Pöschel, Jürgen author SpringerLink (Online service) |
| 件 名 | LCSH:Popular works LCSH:Mathematics LCSH:Dynamics LCSH:Ergodic theory LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Partial differential equations LCSH:Physics LCSH:Education FREE:Popular Science FREE:Popular Science in Education FREE:Global Analysis and Analysis on Manifolds FREE:Mathematics, general FREE:Dynamical Systems and Ergodic Theory FREE:Partial Differential Equations FREE:Mathematical Methods in Physics |
| 分 類 | DC23:370 |
| 巻冊次 | ISBN:9783662080542 
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| ISBN | 9783662080542 |
| URL | http://dx.doi.org/10.1007/978-3-662-08054-2 |
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