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Solitons and the inverse scattering transform / Mark J. Ablowitz and Harvey Segur

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Publisher number: AM04Language: English Series: Society for Industrial and Applied Mathematics. SIAM studies in applied and numerical mathematics ; 4Publisher: Philadelphia, Pa : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1981Description: Online-Ressource (1 electronic text x, 425 p.)ISBN:
  • 9780898714777
  • 089871477X
  • 9781611970883
  • 9781611970883
  • 089871177X
  • 9780898714777
Subject(s): Additional physical formats: Erscheint auch als: No title DruckAusgabeDDC classification:
  • 515.3/5 19
LOC classification:
  • QA927
DOI: DOI: 10.1137/1.9781611970883Online resources: Additional physical formats: Also available in print version.
Contents:
Includes bibliographical references (p. 393-414) and indexes
Chapter 1: The inverse scattering transform on the infinite interval -- Chapter 2: IST in other settings -- Chapter 3: Other perspectives -- Chapter 4: Applications.
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 solutionsPPN: PPN: 722016956Package identifier: Produktsigel: ZDB-72-SIA
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