The Discrete Nonlinear Schr Dinger Equation

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The Discrete Nonlinear Schr Dinger Equation

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Author : Panayotis G. Kevrekidis
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-07

The Discrete Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-07 with Science categories.

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.

Discrete And Continuous Nonlinear Schr Dinger Systems

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Author : M. J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2004

Discrete And Continuous Nonlinear Schr Dinger Systems written by M. J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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.

Handbook Of Exact Solutions To The Nonlinear Schrodinger Equations

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Author : Usama Al Khawaja
language : en
Publisher: IOP Publishing Limited
Release Date : 2024-09-30

Handbook Of Exact Solutions To The Nonlinear Schrodinger Equations written by Usama Al Khawaja and has been published by IOP Publishing Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-30 with Science categories.

This book aims to organise and centralise existing solutions of the nonlinear Schrödinger equation (NLSE). This expanded second edition contains new solutions published or derived since the first edition. Noting the increasing interest in and applications of the fractional nonlinear Schrödinger equation, a new chapter devoted to this topic has been added.

Existence Of A Solution To The Discrete Nonlinear Schr Dinger Equation

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Author : Santhosh Heddese
language : en
Publisher:
Release Date : 2004

Existence Of A Solution To The Discrete Nonlinear Schr Dinger Equation written by Santhosh Heddese and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

The Nonlinear Schr Dinger Equation

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Author : Gadi Fibich
language : en
Publisher: Springer
Release Date : 2015-03-06

The Nonlinear Schr Dinger Equation written by Gadi Fibich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-06 with Mathematics categories.

This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France

On The Discrete Nonlinear Schr Dinger Equation With Pt Symmetry

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Author : Amal Jasim Mohammed
language : en
Publisher:
Release Date : 2018

On The Discrete Nonlinear Schr Dinger Equation With Pt Symmetry written by Amal Jasim Mohammed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Semilinear Schrodinger Equations

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Author : Thierry Cazenave
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Semilinear Schrodinger Equations written by Thierry Cazenave and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.

Solitons And The Inverse Scattering Transform

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Author : Mark J. Ablowitz
language : en
Publisher: SIAM
Release Date : 2006-05-15

Solitons And The Inverse Scattering Transform written by Mark J. Ablowitz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-15 with Mathematics categories.

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.

Proceedings Of The Workshop On Nonlinearity Integrability And All That Twenty Years After Needs 79

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Author : M. Boiti
language : en
Publisher: World Scientific
Release Date : 2000

Proceedings Of The Workshop On Nonlinearity Integrability And All That Twenty Years After Needs 79 written by M. Boiti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.

This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems ? classical and quantum ? are considered.

Ultra Slow Dynamics Of Localised Modes In The Discrete Nonlinear Schr Dinger Equation

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Author : Liviu Florin Chirondojan
language : en
Publisher:
Release Date : 2019

Ultra Slow Dynamics Of Localised Modes In The Discrete Nonlinear Schr Dinger Equation written by Liviu Florin Chirondojan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.