[PDF] A Numerical Study Of The Nonlinear Schrodinger Equation eBook

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Solitons and the Inverse Scattering Transform

Mark J. Ablowitz
Solitons and the Inverse Scattering Transform by Mark J. Ablowitz PDF

Author : Mark J. Ablowitz
Publisher : SIAM
Page : 433 pages
File Size : 16,41 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.

The Discrete Nonlinear Schrödinger Equation

Panayotis G. Kevrekidis
The Discrete Nonlinear Schrödinger Equation by Panayotis G. Kevrekidis PDF

Author : Panayotis G. Kevrekidis
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 21,13 MB
Release : 2009-07-07
Category : Science
ISBN : 3540891994

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This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.