The Nonlinear Schr Dinger Equation
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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.
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
The Nonlinear Schr Dinger Equation
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Author : Nalan Antar
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-07-06
The Nonlinear Schr Dinger Equation written by Nalan Antar and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Mathematics categories.
The nonlinear Schrödinger equation is a prototypical dispersive nonlinear partial differential equation that has been derived in many areas of physics and analyzed mathematically for many years. With this book, we aim to capture different perspectives of researchers on the nonlinear Schrödinger equation arising from theoretical, numerical, and experimental aspects. The eight chapters cover a variety of topics related to nonlinear optics, quantum mechanics, and physics. This book provides scientists, researchers, and engineers as well as graduate and post-graduate students working on or interested in the nonlinear Schrödinger equation with an in-depth discussion of the latest advances in nonlinear optics and quantum physics.
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.
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.
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.
The Nonlinear Schrodinger Equation
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Author :
language : en
Publisher:
Release Date : 1995
The Nonlinear Schrodinger Equation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Hamiltonian systems categories.
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.
Introduction To Nonlinear Dispersive Equations
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Author : Felipe Linares
language : en
Publisher: Springer
Release Date : 2014-12-15
Introduction To Nonlinear Dispersive Equations written by Felipe Linares and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.