Solitons and the inverse scattering transform:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1981
|
| Schriftenreihe: | SIAM studies in applied mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 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 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 |
| Beschreibung: | 1 Online-Ressource (x, 425 Seiten, [2] s. of Platte) |
| ISBN: | 9780898714777 |
| DOI: | 10.1137/1.9781611970883 |
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| 500 | |a Includes bibliographical references (s. 393-414) and indexes | ||
| 500 | |a Chapter 1: The inverse scattering transform on the infinite interval -- Chapter 2: IST in other settings -- Chapter 3: Other perspectives -- Chapter 4: Applications | ||
| 500 | |a 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 | ||
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| discipline | Physik |
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| isbn | 9780898714777 |
| language | English |
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| spelling | Ablowitz, Mark J. 1945- Verfasser (DE-588)143611844 aut Solitons and the inverse scattering transform Mark J. Ablowitz and Harvey Segur Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 1981 1 Online-Ressource (x, 425 Seiten, [2] s. of Platte) txt rdacontent c rdamedia cr rdacarrier SIAM studies in applied mathematics 4 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 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 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 Solitons Inverse scattering transform Soliton (DE-588)4135213-0 gnd rswk-swf Inverse Streutheorie (DE-588)4561758-2 gnd rswk-swf Strahlung (DE-588)4057849-5 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Inverse Streutheorie (DE-588)4561758-2 s Soliton (DE-588)4135213-0 s DE-604 Strahlung (DE-588)4057849-5 s 1\p DE-604 Wellengleichung (DE-588)4065315-8 s 2\p DE-604 Segur, Harvey Sonstige (DE-588)106397822X oth Erscheint auch als Druckausgabe 9780898714777 SIAM studies in applied mathematics 4 (DE-604)BV047229985 4 https://doi.org/10.1137/1.9781611970883 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ablowitz, Mark J. 1945- Solitons and the inverse scattering transform SIAM studies in applied mathematics Solitons Inverse scattering transform Soliton (DE-588)4135213-0 gnd Inverse Streutheorie (DE-588)4561758-2 gnd Strahlung (DE-588)4057849-5 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4135213-0 (DE-588)4561758-2 (DE-588)4057849-5 (DE-588)4065315-8 |
| title | Solitons and the inverse scattering transform |
| title_auth | Solitons and the inverse scattering transform |
| title_exact_search | Solitons and the inverse scattering transform |
| title_full | Solitons and the inverse scattering transform Mark J. Ablowitz and Harvey Segur |
| title_fullStr | Solitons and the inverse scattering transform Mark J. Ablowitz and Harvey Segur |
| title_full_unstemmed | Solitons and the inverse scattering transform Mark J. Ablowitz and Harvey Segur |
| title_short | Solitons and the inverse scattering transform |
| title_sort | solitons and the inverse scattering transform |
| topic | Solitons Inverse scattering transform Soliton (DE-588)4135213-0 gnd Inverse Streutheorie (DE-588)4561758-2 gnd Strahlung (DE-588)4057849-5 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Solitons Inverse scattering transform Soliton Inverse Streutheorie Strahlung Wellengleichung |
| url | https://doi.org/10.1137/1.9781611970883 |
| volume_link | (DE-604)BV047229985 |
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