Schr Dinger Equations In Nonlinear Systems

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Schr Dinger Equations In Nonlinear Systems

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Author : Wu-Ming Liu
language : en
Publisher: Springer
Release Date : 2019-03-20

Schr Dinger Equations In Nonlinear Systems written by Wu-Ming Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

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.

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.

The Nonlinear Schr Dinger Equation

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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-18

The Nonlinear Schr Dinger Equation written by Catherine Sulem 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 1999-06-18 with Mathematics categories.

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Global Solutions Of Nonlinear Schr Dinger Equations

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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date :

Global Solutions Of Nonlinear Schr Dinger Equations written by Jean Bourgain 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 with Science categories.

Optical Communication Theory And Techniques

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Author : Enrico Forestieri
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-26

Optical Communication Theory And Techniques written by Enrico Forestieri 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 2006-01-26 with Computers categories.

Since the advent of optical communications, a greattechnological effort has been devoted to the exploitation of the huge bandwidth of optical fibers. Sta- ing from a few Mb/s single channel systems, a fast and constant technological development has led to the actual 10 Gb/s per channel dense wavelength - vision multiplexing (DWDM) systems, with dozens of channels on a single fiber. Transmitters and receivers are now ready for 40 Gb/s, whereas hundreds of channels can be simultaneously amplified by optical amplifiers. Nevertheless, despite such a pace in technological progress, optical c- munications are still in a primitive stage if compared, for instance, to radio communications: the widely spread on-off keying (OOK) modulation format is equivalent to the rough amplitude modulation (AM) format, whereas the DWDM technique is nothing more than the optical version of the frequency - vision multiplexing (FDM) technique. Moreover, adaptive equalization, ch- nel coding or maximum likelihood detection are still considered something “exotic” in the optical world. This is mainly due to the favourable char- teristics of the fiber optic channel (large bandwidth, low attenuation, channel stability, ...), which so far allowed us to use very simple transmission and detection techniques.

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.

Nonlinear Waves In Integrable And Non Integrable Systems

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Author : Jianke Yang
language : en
Publisher: SIAM
Release Date : 2010-12-02

Nonlinear Waves In Integrable And Non Integrable Systems written by Jianke Yang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Science categories.

Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).

Nonlinear Systems And Their Remarkable Mathematical Structures

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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2021-09-07

Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

The Nonlinear Schr Dinger Equation

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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30

The Nonlinear Schr Dinger Equation written by Catherine Sulem 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 2007-06-30 with Mathematics categories.

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.