Solitons and the inverse scattering transform
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The work Solitons and the inverse scattering transform represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Solitons and the inverse scattering transform
Resource Information
The work Solitons and the inverse scattering transform represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Solitons and the inverse scattering transform
 Statement of responsibility
 Mark J. Ablowitz and Harvey Segur
 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 pulselike 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
 Additional physical form
 Also available in print version.
 Cataloging source
 CaBNVSL
 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
 Series statement
 SIAM studies in applied mathematics
 Series volume
 4
 Target audience
 adult
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