The Resource Solitons and the inverse scattering transform, Mark J. Ablowitz and Harvey Segur, (electronic resource)

Solitons and the inverse scattering transform, Mark J. Ablowitz and Harvey Segur, (electronic resource)

Label
Solitons and the inverse scattering transform
Title
Solitons and the inverse scattering transform
Statement of responsibility
Mark J. Ablowitz and Harvey Segur
Creator
Contributor
Subject
Language
eng
Summary
A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods. Chapters 1 and 2 of the book describe in detail the theory of the inverse scattering transform. Chapter 3 discusses alternate methods for these exactly solvable problems and the interconnections among them. Physical applications are described in Chapter 4, where, for example, similarities between deep water waves and nonlinear optics become evident. Because of the fundamental role of linear theory, there is an extensive appendix that addresses the linear problems and their solutions
Member of
Additional physical form
Also available in print version.
Cataloging source
CaBNVSL
http://library.link/vocab/creatorName
Ablowitz, Mark J
Dewey number
515.3/5
Illustrations
  • illustrations
  • plates
Index
index present
LC call number
QA927
LC item number
.A34 1981eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Segur, Harvey
  • Society for Industrial and Applied Mathematics
Series statement
SIAM studies in applied mathematics
Series volume
4
http://library.link/vocab/subjectName
  • Solitons
  • Inverse scattering transform
Target audience
adult
Label
Solitons and the inverse scattering transform, Mark J. Ablowitz and Harvey Segur, (electronic resource)
Link
http://libraries.ou.edu/access.aspx?url=http://epubs.siam.org/ebooks/siam/studies_in_applied_and_numerical_mathematics/am04
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 393-414) and indexes
Color
black and white
Contents
Chapter 1: The inverse scattering transform on the infinite interval -- Chapter 2: IST in other settings -- Chapter 3: Other perspectives -- Chapter 4: Applications
Dimensions
unknown
Extent
1 electronic text (x, 425 p., [2] p. of plates)
File format
multiple file formats
Form of item
online
Governing access note
Restricted to subscribers or individual electronic text purchasers
Isbn
9781611970883
Isbn Type
(electronic bk.)
Other physical details
ill. (some col.), digital file.
Publisher number
AM04
Reformatting quality
access
Specific material designation
remote
System control number
  • 3862391-01okla_normanlaw
  • (SIRSI)3862391
  • (Sirsi) i9781611970883
  • (CaBNVSL)gtp00547217
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader
Label
Solitons and the inverse scattering transform, Mark J. Ablowitz and Harvey Segur, (electronic resource)
Link
http://libraries.ou.edu/access.aspx?url=http://epubs.siam.org/ebooks/siam/studies_in_applied_and_numerical_mathematics/am04
Publication
Bibliography note
Includes bibliographical references (p. 393-414) and indexes
Color
black and white
Contents
Chapter 1: The inverse scattering transform on the infinite interval -- Chapter 2: IST in other settings -- Chapter 3: Other perspectives -- Chapter 4: Applications
Dimensions
unknown
Extent
1 electronic text (x, 425 p., [2] p. of plates)
File format
multiple file formats
Form of item
online
Governing access note
Restricted to subscribers or individual electronic text purchasers
Isbn
9781611970883
Isbn Type
(electronic bk.)
Other physical details
ill. (some col.), digital file.
Publisher number
AM04
Reformatting quality
access
Specific material designation
remote
System control number
  • 3862391-01okla_normanlaw
  • (SIRSI)3862391
  • (Sirsi) i9781611970883
  • (CaBNVSL)gtp00547217
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader

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