Coverart for item
The Resource Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow

Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow

Label
Spectral and dynamical stability of nonlinear waves
Title
Spectral and dynamical stability of nonlinear waves
Statement of responsibility
Todd Kapitula, Keith Promislow
Creator
Contributor
Subject
Language
eng
Summary
This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Kapitula, Todd
Dewey number
515/.353
Index
index present
LC call number
QA927
LC item number
.K37 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1964-
http://library.link/vocab/relatedWorkOrContributorName
Promislow, Keith
Series statement
Applied mathematical sciences,
Series volume
v. 185
http://library.link/vocab/subjectName
  • Nonlinear waves
  • Nonlinear wave equations
  • Nonlinear wave equations
  • Nonlinear waves
Label
Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • The Evans Function for Sturm-Liouville Operators on the Real Line
  • The Evans Function for nth-Order Operators on the Real Line
  • Introduction
  • Background Material and Notation
  • Essential and Absolute Spectra
  • Asymptotic Stability of Waves in Dissipative Systems
  • Orbital Stability of Waves in Hamiltonian Systems
  • Point Spectrum: Reduction to Finite-Rank Eigenvalue Problems
  • Point Spectrum: Linear Hamiltonian Systems
  • The Evans Function for Boundary-Value Problems
Control code
849317905
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781461469957
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4614-6995-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)849317905
Label
Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • The Evans Function for Sturm-Liouville Operators on the Real Line
  • The Evans Function for nth-Order Operators on the Real Line
  • Introduction
  • Background Material and Notation
  • Essential and Absolute Spectra
  • Asymptotic Stability of Waves in Dissipative Systems
  • Orbital Stability of Waves in Hamiltonian Systems
  • Point Spectrum: Reduction to Finite-Rank Eigenvalue Problems
  • Point Spectrum: Linear Hamiltonian Systems
  • The Evans Function for Boundary-Value Problems
Control code
849317905
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781461469957
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4614-6995-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)849317905

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      38.944491 -92.326012
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