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  • Licensed  (5)
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  • Licensed  (5)
  • 1
    Online Resource
    Online Resource
    Solitons and the inverse scattering transform (1981)
    Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
    Details
    UID:
    b3kat_BV039747222
    Format: 1 Online-Ressource (x, 425 Seiten, [2] s. of Platte)
    ISBN: 9780898714777
    Series Statement: SIAM studies in applied mathematics 4
    Note: 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
    Additional Edition: Erscheint auch als Druckausgabe ISBN 9780898714777
    Language: English
    Keywords: Inverse Streutheorie ; Soliton ; Strahlung ; Wellengleichung
    DOI: 10.1137/1.9781611970883
    URL: Volltext
    Author information: Ablowitz, Mark J. 1945-
    Library Location Call Number Volume/Issue/Year Availability
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    TU Berlin
  • 2
    Online Resource
    Online Resource
    Complex variables : introduction and applications (2003)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_883326345
    Format: 1 Online-Ressource (xii, 647 pages) , digital, PDF file(s)
    Edition: Second edition
    ISBN: 9780511791246
    Series Statement: Cambridge texts in applied mathematics 35
    Content: Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann–Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015)
    Additional Edition: ISBN 9780521534291
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780521534291
    Language: English
    DOI: 10.1017/CBO9780511791246
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
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    Online Resource
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    Open Access Request
    UB Potsdam
  • 3
    Online Resource
    Online Resource
    Nonlinear dispersive waves : asymptotic analysis and solitons (2011)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_88333352X
    Format: 1 Online-Ressource (xiv, 348 pages) , digital, PDF file(s)
    ISBN: 9780511998324
    Series Statement: Cambridge texts in applied mathematics 47
    Content: The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science
    Content: Machine generated contents note: Preface; Acknowledgements; Part I. Fundamentals and Basic Applications: 1. Introduction; 2. Linear and nonlinear wave equations; 3. Asymptotic analysis of wave equations; 4. Perturbation analysis; 5. Water waves and KdV type equations; 6. Nonlinear Schrödinger models and water waves; 7. Nonlinear Schrödinger models in nonlinear optics; Part II. Integrability and Solitons: 8. Solitons and integrable equations; 9. Inverse scattering transform for the KdV equation; Part III. Novel Applications of Nonlinear Waves: 10. Communications; 11. Mode-locked lasers; 12. Nonlinear photonic lattices; References; Index
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015)
    Additional Edition: ISBN 9781107012547
    Additional Edition: ISBN 9781107664104
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9781107012547
    Language: English
    DOI: 10.1017/CBO9780511998324
    URL: Volltext
    URL: Inhaltstext
    URL: Inhaltsverzeichnis
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    Online Resource
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    UB Potsdam
  • 4
    Online Resource
    Online Resource
    Solitons, nonlinear evolution equations and inverse scattering (1991)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_883334739
    Format: 1 Online-Ressource (xii, 516 pages) , digital, PDF file(s).
    ISBN: 9780511623998
    Series Statement: London Mathematical Society lecture note series 149
    Content: Solitons have been of considerable interest to mathematicians since their discovery by Kruskal and Zabusky. This book brings together several aspects of soliton theory currently only available in research papers. Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ method. Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015)
    Additional Edition: ISBN 9780521387309
    Additional Edition: ISBN 9780521387309
    Additional Edition: ISBN 9780521387309
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780521387309
    Language: English
    DOI: 10.1017/CBO9780511623998
    URL: Volltext
    URL: Inhaltstext
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    UB Potsdam
  • 5
    Online Resource
    Online Resource
    Discrete and continuous nonlinear Schrödinger systems (2004)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_883359499
    Format: 1 Online-Ressource (ix, 257 pages) , digital, PDF file(s).
    ISBN: 9780511546709
    Series Statement: London Mathematical Society lecture note series 302
    Content: In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015) , 1. Introduction -- 2. Nonlinear Schrd̲inger equation (NLS) -- 3. Integrable discrete nonlinear Schrd̲inger equation (IDNLS) -- 4. Matrix nonlinear Schrd̲inger equation (MNLS) -- 5 Integrable discrete matrix NLS equation (IDMNLS).
    Additional Edition: ISBN 9780521534376
    Additional Edition: ISBN 9780521534376
    Additional Edition: ISBN 9780521534376
    Additional Edition: Erscheint auch als Ablowitz, Mark J., 1945 - Discrete and continuous nonlinear Schrödinger systems Cambridge [u.a.] : Cambridge University Press, 2004 ISBN 0521534372
    Additional Edition: Print version ISBN 9780521534376
    Language: English
    Subjects: Mathematics
    RVK:
    SI 320
    Keywords: Nichtlineare Schrödinger-Gleichung ; Inverse Streutheorie ; Nichtlineare Schrödinger-Gleichung ; Inverse Streutheorie
    DOI: 10.1017/CBO9780511546709
    URL: Volltext
    URL: Inhaltstext
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    Online Resource
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    UB Potsdam
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