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Field name	Details
Dewey Class	515.39
Title	KdV & KAM ([EBook]) / by Thomas Kappeler, Jürgen Pöschel.
Author	Kappeler, Thomas
Added Personal Name	Pöschel, Jürgen
Other name(s)	SpringerLink (Online service)
Edition statement	3. Folge.
Publication	Berlin, Heidelberg : Springer , 2003.
Physical Details	XIII, 279 pages : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 0071-1136 ; ; 45
ISBN	9783662080542
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-08054-2
Links to Related Works	Subject References: Boundary value problems . Differentiable dynamical systems . Dynamical systems and ergodic theory . Ergodic theory . Global analysis (Mathematics) . Manifolds (Mathematics) . Mathematical Methods in Physics . Partial differential equations . Perturbation (Mathematics) . Authors: author . Kappeler, Thomas . Pöschel, Jürgen . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics . Classification: 515.39 . 515.39 (DDC 23) .

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KdV & KAM

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