[PDF] Solitons And The Inverse Scattering Transform eBook

Author : Mark J. Ablowitz
Publisher : SIAM
Page : 433 pages
File Size : 48,49 MB
Release : 2006-05-15
Category : Mathematics
ISBN : 089871477X

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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 localised 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.

Author : W. Eckhaus
Publisher : Elsevier
Page : 235 pages
File Size : 50,40 MB
Release : 2011-08-18
Category : Mathematics
ISBN : 0080871615

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The Inverse Scattering Transformation and The Theory of Solitons

Author : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 532 pages
File Size : 37,42 MB
Release : 1991-12-12
Category : Mathematics
ISBN : 0521387302

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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.

Author : Robert M. Miura
Publisher : Springer
Page : 302 pages
File Size : 35,93 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540382208

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Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974

Author : B G Konopelchenko
Publisher : World Scientific
Page : 304 pages
File Size : 40,44 MB
Release : 1993-04-30
Category :
ISBN : 9814518069

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The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.

Author : R.K. Bullough
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 46,38 MB
Release : 2013-11-11
Category : Science
ISBN : 3642814484

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With contributions by numerous experts

Author : P. G. Drazin
Publisher : Cambridge University Press
Page : 244 pages
File Size : 26,42 MB
Release : 1989-02-09
Category : Mathematics
ISBN : 9780521336550

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This textbook is an introduction to the theory of solitons in the physical sciences.

Author : J. L. Bona
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 23,12 MB
Release : 2002
Category : Mathematics
ISBN : 0821831615

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Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant inexperimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even morepossibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ``Legacy of the Inverse Scattering Transform'' held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ``Reviews''. This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects ofsoliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided aforum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.