The Resource KdV & KAM, by Thomas Kappeler, Jürgen Pöschel, (electronic resource)

KdV & KAM, by Thomas Kappeler, Jürgen Pöschel, (electronic resource)

Label
KdV & KAM
Title
KdV & KAM
Statement of responsibility
by Thomas Kappeler, Jürgen Pöschel
Creator
Contributor
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
AU@
http://library.link/vocab/creatorName
Kappeler, Thomas
Dewey number
514.74
Index
no index present
LC call number
QA614-614.97
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Pöschel, Jürgen
Series statement
Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics,
Series volume
45
http://library.link/vocab/subjectName
  • Mathematics
  • Differentiable dynamical systems
  • Global analysis
  • Differential equations, Partial
  • Mathematical physics
Label
KdV & KAM, by Thomas Kappeler, Jürgen Pöschel, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-662-08054-2
Instantiates
Publication
Antecedent source
file reproduced from original
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
3. Folge.
Extent
1 online resource (xiii, 280 pages).
File format
unknown
Form of item
online
Isbn
9783662080542
Isbn Type
(electronic bk.)
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-08054-2
Quality assurance targets
unknown
Reformatting quality
access
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)851390493
  • (OCoLC)ocn851390493
Label
KdV & KAM, by Thomas Kappeler, Jürgen Pöschel, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-662-08054-2
Publication
Antecedent source
file reproduced from original
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
3. Folge.
Extent
1 online resource (xiii, 280 pages).
File format
unknown
Form of item
online
Isbn
9783662080542
Isbn Type
(electronic bk.)
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-08054-2
Quality assurance targets
unknown
Reformatting quality
access
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)851390493
  • (OCoLC)ocn851390493

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