The Nonlinear Schr Dinger Equation
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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.
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.
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.
Global Solutions Of Nonlinear Schrodinger Equations
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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Global Solutions Of Nonlinear Schrodinger 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 1999 with Differential equations, Partial categories.
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
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.
Nonlinear Schrodinger Equation
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Author : Catherine Sulem
language : en
Publisher:
Release Date : 1999-05-01
Nonlinear Schrodinger Equation written by Catherine Sulem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-01 with categories.
Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition
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Author : Remi Carles
language : en
Publisher: World Scientific
Release Date : 2020-10-05
Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition written by Remi Carles and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-05 with Mathematics categories.
The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces.The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.
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.
Korteweg De Vries And Nonlinear Schr Dinger Equations Qualitative Theory
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Author : Peter E. Zhidkov
language : en
Publisher: Springer
Release Date : 2003-07-01
Korteweg De Vries And Nonlinear Schr Dinger Equations Qualitative Theory written by Peter E. Zhidkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).